{"id":26536,"date":"2023-03-19T16:09:22","date_gmt":"2023-03-19T16:09:22","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26536"},"modified":"2024-03-15T06:17:35","modified_gmt":"2024-03-15T06:17:35","slug":"common-difference-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference","title":{"rendered":"Common Difference: Definition with Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-ab49c3bf-359f-46b0-ac36-ab5d37078c81\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference#0-what-is-the-common-difference-of-an-arithmetic-sequence>What is the Common Difference of an Arithmetic Sequence?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference#2-how-to-find-the-common-difference-of-an-arithmetic-sequence>How to Find the Common Difference of an Arithmetic Sequence<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference#4-facts-about-common-difference>Facts about Common Difference<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference#6-solved-examples-for-common-difference>Solved Examples for Common Difference<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference#7-practice-problems-on-common-difference>Practice Problems on Common Difference<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference#8-frequently-asked-questions-on-common-difference>Frequently Asked Questions on Common Difference<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-common-difference-of-an-arithmetic-sequence\">What is the Common Difference of an Arithmetic Sequence?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>An arithmetic sequence is a sequence of numbers in which the difference between two consecutive numbers is always constant. This difference is called a common difference of the arithmetic sequence.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, 1, 3, 5, 7, 9, \u2026 is an arithmetic sequence.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the difference between any two consecutive terms is 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">More examples of an arithmetic sequence are as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">0, 2, 4, 6, 8, 10, 12, \u2026<\/p>\n\n\n\n<p class=\"eplus-wrapper\">4, 7, 10, 13, &#8230;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">60, 55, 50, 45, 40, &#8230;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-common-difference-definition\">Common Difference: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The common difference in arithmetic sequences is the difference between any two consecutive terms (difference between any term and its previous term) which is always constant. You can get the consecutive terms of an arithmetic sequence by adding the common difference to the previous term. It is usually denoted by \u201cd.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us understand the common difference in math and other terminologies in arithmetic sequence with an example. Imagine you want to buy a mountain bike that costs $\\$150$. Your mother gave you an initial amount of $\\$50$ to start your savings. Each month, you save $\\$25$ from your pocket money to add to your savings. This can be represented as an arithmetic sequence as follows.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"357\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/common-difference-in-arithmetic-sequence-visual-example.png\" alt=\"Common difference in arithmetic sequence visual example\" class=\"wp-image-40962\" title=\"Common difference in arithmetic sequence visual example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/common-difference-in-arithmetic-sequence-visual-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/common-difference-in-arithmetic-sequence-visual-example-300x173.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We can see that the sequence 50, 75, 100, 125, 150 is an arithmetic sequence with the common difference, $d = 25$.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/calculate-the-difference-between-amounts-of-money\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_sub_word_prob_2_pt.png\" alt=\"Calculate the Difference Between Amounts of Money Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Calculate the Difference Between Amounts of Money Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-difference\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/rec_add_sub_facts_find_missing_difference_6_pt.png\" alt=\"Choose the Correct Difference Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Correct Difference Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/cross-out-fractions-to-find-the-difference\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_represent_sub_models_pt.png\" alt=\"Cross Out Fractions to Find the Difference Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Cross Out Fractions to Find the Difference Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/cross-out-parts-to-find-the-difference-between-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_represent_sub_greater_than_1_models_pt.png\" alt=\"Cross out Parts to Find the Difference Between Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Cross out Parts to Find the Difference Between Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/cross-out-to-find-the-difference-between-a-mixed-number-and-a-fraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_represent_sub_mixed_num_models_pt.png\" alt=\"Cross Out to FInd the Difference Between a Mixed Number and a Fraction Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Cross Out to FInd the Difference Between a Mixed Number and a Fraction Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-the-correct-difference\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/rec_add_sub_facts_find_missing_difference_9_pt.png\" alt=\"Determine the Correct Difference Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine the Correct Difference Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-the-difference-and-match\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/rec_add_sub_facts_mix_match_differences_7_pt.png\" alt=\"Determine the Difference and Match Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine the Difference and Match Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-the-difference\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/rec_add_sub_facts_find_missing_difference_3_pt.png\" alt=\"Determine the Difference Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine the Difference Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-the-difference-to-match\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/rec_add_sub_facts_mix_match_differences_8_pt.png\" alt=\"Determine the Difference to Match Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine the Difference to Match Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/estimate-the-difference\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_estimate_diff_pt.png\" alt=\"Estimate the Difference Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Estimate the Difference Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-how-to-find-the-common-difference-of-an-arithmetic-sequence\">How to Find the Common Difference of an Arithmetic Sequence<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">For an arithmetic sequence $\\left\\{a_1, a_2, a_3, \u2026 a_{n-1}, a_n\\right\\}$, where <em>n <\/em>is the total number of terms in the sequence, the common difference \u201cd\u201d<em> <\/em>will be equal to the difference between any n<sup>th<\/sup> term and $(n-1)^{th}$ term, where n = 2, 3, 4, \u2026, n.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = a_2\\;-\\;a_1 = a_3\\;-\\;a_2\\;&nbsp; &#8230; = a_n\\;-\\;a_{n-1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For the sequence$ \\left\\{50, 75, 100, 125, 150\\right\\},\\; d = 75\\;-\\;50 = 100\\;-\\;75 = 125\\;-\\;100 = 150\\;-\\;125 = 25$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-common-difference-formula\">Common Difference Formula<\/h3>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When two consecutive terms in the sequence are given:<br>$d = a_n\\;-\\;a_{n-1}$, where an (the n<sup>th<\/sup> term) and $a_{n-1}$ (the previous term) are consecutive terms in the sequence.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the first and the last terms of the arithmetic sequence and the total number of terms are given:<br>$d = \\frac{a_n-a_1}{n-1}<em>, <\/em>where <em>an<\/em> is the last term of the sequence, $a_1$ is the first term in the sequence, and <em>n <\/em>is the total number of terms in the sequence.<\/li>\n<\/ul>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-fractions-by-finding-common-denominator\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-fractions-by-finding-common-denominator.jpeg\" alt=\"Compare Fractions by Finding Common Denominator Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/difference-between-mixed-number-and-fraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/difference-between-mixed-number-and-fraction.jpeg\" alt=\"Difference Between Mixed Number and Fraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/difference-of-mixed-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/difference-of-mixed-numbers.jpeg\" alt=\"Difference of Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/difference-of-unlike-fractions-and-mixed-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/difference-of-unlike-fractions-and-mixed-numbers.jpeg\" alt=\"Difference of Unlike Fractions and Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/difference-of-unlike-mixed-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/difference-of-unlike-mixed-numbers.jpeg\" alt=\"Difference of Unlike Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/estimate-the-sum-or-the-difference\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/estimate-the-sum-or-the-difference.jpeg\" alt=\"Estimate the Sum or the Difference Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-100\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-100.jpeg\" alt=\"Even Difference in Subtraction Expressions Within 100\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-20\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-20.jpeg\" alt=\"Even Difference in Subtraction Expressions Within 20\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-50\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-50.jpeg\" alt=\"Even Difference in Subtraction Expressions Within 50\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-common-denominator-compare-unlike-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/find-common-denominator-compare-unlike-fractions.jpeg\" alt=\"Find Common Denominator & Compare Unlike Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-facts-about-common-difference\">Facts about Common Difference<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">It is denoted by the letter <em>d.<\/em>&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">It is positive in an increasing arithmetic sequence.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">It is negative in a decreasing arithmetic sequence.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">For a constant sequence, the common difference is 0.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Example: 3, 3, 3, 3, 3, \u2026<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The common difference in arithmetic sequences is the difference between their two consecutive terms. For an arithmetic sequence, it is always constant. It is denoted by the letter <em>&#8216;d&#8217;.<\/em> It can be negative, positive, or zero.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Learn more mathematical concepts on SplashLearn, the game-based learning platform equipped with interactive games and fun worksheets.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-for-common-difference\">Solved Examples for Common Difference<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Find the common difference of the sequence:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">32, 26, 20, 14, \u2026<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> We can find the common difference by subtracting each pair of consecutive terms.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = 26\\;-\\;32 = 20\\;-\\;26 = 14\\;-\\;20 = \\;-6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the common difference of the given sequence is -6.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Find the common difference of the arithmetic sequence <\/strong>$-\\;\\frac{1}{2},\\; \\frac{3}{2},\\; \\frac{7}{2},\\;\\frac{11}{2},\\; &#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>We can find the common difference by subtracting each pair of consecutive terms.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = \\frac{3}{2}\\;-\\;\\bigg(\\;-\\;\\frac{1}{2}\\bigg) = \\frac{3}{2} + \\frac{1}{2} = \\frac{4}{2} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Also,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = \\frac{7}{2}\\;-\\;\\frac{3}{2} = \\frac{4}{2} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the common difference of the sequence $\\bigg\\{-12,\\; 32,\\; 72,\\;112,\\; &#8230;\\bigg\\}$ is 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. What will be the 15<\/strong><strong><sup>th<\/sup><\/strong><strong> term of an arithmetic progression, if the 13<\/strong><strong><sup>th<\/sup><\/strong><strong> term is 25 and the common difference is 1.5?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>It is given that $a_13 = 25$ and $d = 1.5$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that we can get the next term in an arithmetic sequence by adding the common difference to its previous term.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a_14 = a_13 + d$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a_15 = a_14 + d = a_13 + 2d$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting the given values.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a_15 = 25 + 2(1.5) = 28$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the 15th term of the given arithmetic sequence is 28.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. In the arithmetic sequence <\/strong>$\\left\\{k + 8, k^2 , 3k\\;-\\;2, 5k\\;\u2212\\;10, 2k\\;-\\;3\\right\\}$,<strong> if <\/strong>$k = 3$<strong>, then find the common difference.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>We can find the common difference by subtracting each pair of consecutive terms. To find the terms in the arithmetic sequences, let\u2019s substitute 3 for k.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given sequence $= \\left\\{3 + 8, 3^2 ,\\; 3 \\times 3\\;-\\;2,\\; 5 \\times3\\;\u2212\\;10,\\; 2 \\times3\\;-\\;3\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given sequence $= \\left\\{11, 9, 7, 5, 3\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, 11 is the first term of the sequence and 9 is the second term of the sequence.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The difference between the first two terms, $11\\;-\\;9 = 2$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the common difference of the given arithmetic sequence is 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. What is the common difference in the following sequence?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\left\\{0.3,0.11,0.19,0.27,0.35\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>We can find the common difference by subtracting each pair of consecutive terms.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = 0.11\\;-\\;0.3 = 0.19\\;-\\;0.11 = 0.27\\;-\\;0.19 = 0.35\\;-\\;0.27 = 0.8$<br>Therefore, 0.8 is the common difference of the sequence $\\left\\{0.3,0.11,0.19,0.27,0.35\\right\\}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-common-difference\">Practice Problems on Common Difference<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Common Difference: Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find the option that does not contain the consecutive terms of an arithmetic sequence.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">13, 34, 55<\/div><div class=\"spq_answer_block\" data-value=\"1\">3, 25, 49<\/div><div class=\"spq_answer_block\" data-value=\"2\">55, 33, 11<\/div><div class=\"spq_answer_block\" data-value=\"3\">28, 40, 552<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 3, 25, 49<br\/>We need to find the difference between the consecutive terms. The option with the unequal difference between the terms is the correct choice.<br>\r\nFor option A:  $34\\;-\\;13 = 55\\;-\\;34 = 21$<br>\r\nFor option B:  $25\\;-\\;3 \\neq 49\\;-\\;25$<br>\r\nFor option C:  $55\\;-\\;33 = 33\\;-\\;11 = 22$<br>\r\nFor option D: $40\\;-\\;28 = 52\\;-\\;40 = 12$<br>\r\nSo, the terms 3, 25, 49 are not the consecutive terms of an arithmetic sequence.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following will be the common difference of the arithmetic sequence containing 35 terms, if its first and last terms are 6 and 108, respectively?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">5<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 3<br\/>It is given that $a_n = 108, \\;a_1 = 6,$ and $n = 35$.<br>\r\nWe know that when the first and the last terms of the arithmetic sequence and the total number of terms are given we use the following formula to find the common difference:<br>\r\n$d = \\frac{a_n-a_1}{n-1}$<br>\r\n$d = \\frac{108-6}{35-1} = \\frac{102}{34} = 3$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is the common difference in the shown arithmetic sequence? $\\left\\{18, 36, 54, 72,...\\right\\}$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">12<\/div><div class=\"spq_answer_block\" data-value=\"1\">14<\/div><div class=\"spq_answer_block\" data-value=\"2\">16<\/div><div class=\"spq_answer_block\" data-value=\"3\">18<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 18<br\/>We can find the common difference by subtracting each pair of consecutive terms.<br>\r\n$d = 36\\;-\\;18 = 54\\;-\\;36 = 72\\;-\\;54 = 18$<br>\r\nTherefore, the common difference of the sequence, $\\left\\{18, 36, 54, 72...\\right\\}$ is 18.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If all the terms of an arithmetic sequence are the same, then its common difference is ___________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">zero<\/div><div class=\"spq_answer_block\" data-value=\"1\">negative<\/div><div class=\"spq_answer_block\" data-value=\"2\">positive<\/div><div class=\"spq_answer_block\" data-value=\"3\">1<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: zero<br\/>If the common difference is zero, all the terms in the sequence will be the same. It is a constant sequence.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which of the following will be the 70th term of an arithmetic progression, If the 71st term is $-277$ and the common difference is 10?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$-267$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$267$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$327$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$-287$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $-287$<br\/>It is given that $a_71 = -277$ and $d = 10$.<br>\r\nWe can get the previous term in an arithmetic sequence by subtracting the common difference from its next term.<br>\r\n$a_70 = a_71\\;-d$<br>\r\n$a_70 = -277\\;-\\;(10) = -287$<br>\r\nSo, the 70th term of the given arithmetic sequence is $-287$.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Common Difference: Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Common Difference\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the option that does not contain the consecutive terms of an arithmetic sequence.\",\n                    \"text\": \"Find the option that does not contain the consecutive terms of an arithmetic sequence.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We need to find the difference between the consecutive terms. The option with the unequal difference between the terms is the correct choice.<br>\r\nFor option A:  $$34\\\\;-\\\\;13 = 55\\\\;-\\\\;34 = 21$$<br>\r\nFor option B:  $$25\\\\;-\\\\;3 \\\\neq 49\\\\;-\\\\;25$$<br>\r\nFor option C:  $$55\\\\;-\\\\;33 = 33\\\\;-\\\\;11 = 22$$<br>\r\nFor option D: $$40\\\\;-\\\\;28 = 52\\\\;-\\\\;40 = 12$$<br>\r\nSo, the terms 3, 25, 49 are not the consecutive terms of an arithmetic sequence.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13, 34, 55\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We need to find the difference between the consecutive terms. The option with the unequal difference between the terms is the correct choice.<br>\r\nFor option A:  $$34\\\\;-\\\\;13 = 55\\\\;-\\\\;34 = 21$$<br>\r\nFor option B:  $$25\\\\;-\\\\;3 \\\\neq 49\\\\;-\\\\;25$$<br>\r\nFor option C:  $$55\\\\;-\\\\;33 = 33\\\\;-\\\\;11 = 22$$<br>\r\nFor option D: $$40\\\\;-\\\\;28 = 52\\\\;-\\\\;40 = 12$$<br>\r\nSo, the terms 3, 25, 49 are not the consecutive terms of an arithmetic sequence.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"55, 33, 11\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We need to find the difference between the consecutive terms. The option with the unequal difference between the terms is the correct choice.<br>\r\nFor option A:  $$34\\\\;-\\\\;13 = 55\\\\;-\\\\;34 = 21$$<br>\r\nFor option B:  $$25\\\\;-\\\\;3 \\\\neq 49\\\\;-\\\\;25$$<br>\r\nFor option C:  $$55\\\\;-\\\\;33 = 33\\\\;-\\\\;11 = 22$$<br>\r\nFor option D: $$40\\\\;-\\\\;28 = 52\\\\;-\\\\;40 = 12$$<br>\r\nSo, the terms 3, 25, 49 are not the consecutive terms of an arithmetic sequence.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"28, 40, 552\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We need to find the difference between the consecutive terms. The option with the unequal difference between the terms is the correct choice.<br>\r\nFor option A:  $$34\\\\;-\\\\;13 = 55\\\\;-\\\\;34 = 21$$<br>\r\nFor option B:  $$25\\\\;-\\\\;3 \\\\neq 49\\\\;-\\\\;25$$<br>\r\nFor option C:  $$55\\\\;-\\\\;33 = 33\\\\;-\\\\;11 = 22$$<br>\r\nFor option D: $$40\\\\;-\\\\;28 = 52\\\\;-\\\\;40 = 12$$<br>\r\nSo, the terms 3, 25, 49 are not the consecutive terms of an arithmetic sequence.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"3, 25, 49\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We need to find the difference between the consecutive terms. The option with the unequal difference between the terms is the correct choice.<br>\r\nFor option A:  $$34\\\\;-\\\\;13 = 55\\\\;-\\\\;34 = 21$$<br>\r\nFor option B:  $$25\\\\;-\\\\;3 \\\\neq 49\\\\;-\\\\;25$$<br>\r\nFor option C:  $$55\\\\;-\\\\;33 = 33\\\\;-\\\\;11 = 22$$<br>\r\nFor option D: $$40\\\\;-\\\\;28 = 52\\\\;-\\\\;40 = 12$$<br>\r\nSo, the terms 3, 25, 49 are not the consecutive terms of an arithmetic sequence.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We need to find the difference between the consecutive terms. The option with the unequal difference between the terms is the correct choice.<br>\r\nFor option A:  $$34\\\\;-\\\\;13 = 55\\\\;-\\\\;34 = 21$$<br>\r\nFor option B:  $$25\\\\;-\\\\;3 \\\\neq 49\\\\;-\\\\;25$$<br>\r\nFor option C:  $$55\\\\;-\\\\;33 = 33\\\\;-\\\\;11 = 22$$<br>\r\nFor option D: $$40\\\\;-\\\\;28 = 52\\\\;-\\\\;40 = 12$$<br>\r\nSo, the terms 3, 25, 49 are not the consecutive terms of an arithmetic sequence.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following will be the common difference of the arithmetic sequence containing 35 terms, if its first and last terms are 6 and 108, respectively?\",\n                    \"text\": \"Which of the following will be the common difference of the arithmetic sequence containing 35 terms, if its first and last terms are 6 and 108, respectively?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"It is given that $$a_n = 108, \\\\;a_1 = 6,$$ and $$n = 35$$.<br>\r\nWe know that when the first and the last terms of the arithmetic sequence and the total number of terms are given we use the following formula to find the common difference:<br>\r\n$$d = \\\\frac{a_n-a_1}{n-1}$$<br>\r\n$$d = \\\\frac{108-6}{35-1} = \\\\frac{102}{34} = 3$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is given that $$a_n = 108, \\\\;a_1 = 6,$$ and $$n = 35$$.<br>\r\nWe know that when the first and the last terms of the arithmetic sequence and the total number of terms are given we use the following formula to find the common difference:<br>\r\n$$d = \\\\frac{a_n-a_1}{n-1}$$<br>\r\n$$d = \\\\frac{108-6}{35-1} = \\\\frac{102}{34} = 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is given that $$a_n = 108, \\\\;a_1 = 6,$$ and $$n = 35$$.<br>\r\nWe know that when the first and the last terms of the arithmetic sequence and the total number of terms are given we use the following formula to find the common difference:<br>\r\n$$d = \\\\frac{a_n-a_1}{n-1}$$<br>\r\n$$d = \\\\frac{108-6}{35-1} = \\\\frac{102}{34} = 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is given that $$a_n = 108, \\\\;a_1 = 6,$$ and $$n = 35$$.<br>\r\nWe know that when the first and the last terms of the arithmetic sequence and the total number of terms are given we use the following formula to find the common difference:<br>\r\n$$d = \\\\frac{a_n-a_1}{n-1}$$<br>\r\n$$d = \\\\frac{108-6}{35-1} = \\\\frac{102}{34} = 3$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"3\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"It is given that $$a_n = 108, \\\\;a_1 = 6,$$ and $$n = 35$$.<br>\r\nWe know that when the first and the last terms of the arithmetic sequence and the total number of terms are given we use the following formula to find the common difference:<br>\r\n$$d = \\\\frac{a_n-a_1}{n-1}$$<br>\r\n$$d = \\\\frac{108-6}{35-1} = \\\\frac{102}{34} = 3$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"It is given that $$a_n = 108, \\\\;a_1 = 6,$$ and $$n = 35$$.<br>\r\nWe know that when the first and the last terms of the arithmetic sequence and the total number of terms are given we use the following formula to find the common difference:<br>\r\n$$d = \\\\frac{a_n-a_1}{n-1}$$<br>\r\n$$d = \\\\frac{108-6}{35-1} = \\\\frac{102}{34} = 3$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the common difference in the shown arithmetic sequence? $$\\\\left\\\\{18, 36, 54, 72,...\\\\right\\\\}$$\",\n                    \"text\": \"Which of the following is the common difference in the shown arithmetic sequence? $$\\\\left\\\\{18, 36, 54, 72,...\\\\right\\\\}$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We can find the common difference by subtracting each pair of consecutive terms.<br>\r\n$$d = 36\\\\;-\\\\;18 = 54\\\\;-\\\\;36 = 72\\\\;-\\\\;54 = 18$$<br>\r\nTherefore, the common difference of the sequence, $$\\\\left\\\\{18, 36, 54, 72...\\\\right\\\\}$$ is 18.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We can find the common difference by subtracting each pair of consecutive terms.<br>\r\n$$d = 36\\\\;-\\\\;18 = 54\\\\;-\\\\;36 = 72\\\\;-\\\\;54 = 18$$<br>\r\nTherefore, the common difference of the sequence, $$\\\\left\\\\{18, 36, 54, 72...\\\\right\\\\}$$ is 18.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We can find the common difference by subtracting each pair of consecutive terms.<br>\r\n$$d = 36\\\\;-\\\\;18 = 54\\\\;-\\\\;36 = 72\\\\;-\\\\;54 = 18$$<br>\r\nTherefore, the common difference of the sequence, $$\\\\left\\\\{18, 36, 54, 72...\\\\right\\\\}$$ is 18.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"16\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We can find the common difference by subtracting each pair of consecutive terms.<br>\r\n$$d = 36\\\\;-\\\\;18 = 54\\\\;-\\\\;36 = 72\\\\;-\\\\;54 = 18$$<br>\r\nTherefore, the common difference of the sequence, $$\\\\left\\\\{18, 36, 54, 72...\\\\right\\\\}$$ is 18.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"18\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We can find the common difference by subtracting each pair of consecutive terms.<br>\r\n$$d = 36\\\\;-\\\\;18 = 54\\\\;-\\\\;36 = 72\\\\;-\\\\;54 = 18$$<br>\r\nTherefore, the common difference of the sequence, $$\\\\left\\\\{18, 36, 54, 72...\\\\right\\\\}$$ is 18.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We can find the common difference by subtracting each pair of consecutive terms.<br>\r\n$$d = 36\\\\;-\\\\;18 = 54\\\\;-\\\\;36 = 72\\\\;-\\\\;54 = 18$$<br>\r\nTherefore, the common difference of the sequence, $$\\\\left\\\\{18, 36, 54, 72...\\\\right\\\\}$$ is 18.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If all the terms of an arithmetic sequence are the same, then its common difference is ___________.\",\n                    \"text\": \"If all the terms of an arithmetic sequence are the same, then its common difference is ___________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If the common difference is zero, all the terms in the sequence will be the same. It is a constant sequence.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"negative\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the common difference is zero, all the terms in the sequence will be the same. It is a constant sequence.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"positive\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the common difference is zero, all the terms in the sequence will be the same. It is a constant sequence.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the common difference is zero, all the terms in the sequence will be the same. It is a constant sequence.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"zero\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If the common difference is zero, all the terms in the sequence will be the same. It is a constant sequence.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If the common difference is zero, all the terms in the sequence will be the same. It is a constant sequence.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following will be the 70th term of an arithmetic progression, If the 71st term is $$-277$$ and the common difference is 10?\",\n                    \"text\": \"Which of the following will be the 70th term of an arithmetic progression, If the 71st term is $$-277$$ and the common difference is 10?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"It is given that $$a_71 = -277$$ and $$d = 10$$.<br>\r\nWe can get the previous term in an arithmetic sequence by subtracting the common difference from its next term.<br>\r\n$$a_70 = a_71\\\\;-d$$<br>\r\n$$a_70 = -277\\\\;-\\\\;(10) = -287$$<br>\r\nSo, the 70th term of the given arithmetic sequence is $$-287$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-267$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is given that $$a_71 = -277$$ and $$d = 10$$.<br>\r\nWe can get the previous term in an arithmetic sequence by subtracting the common difference from its next term.<br>\r\n$$a_70 = a_71\\\\;-d$$<br>\r\n$$a_70 = -277\\\\;-\\\\;(10) = -287$$<br>\r\nSo, the 70th term of the given arithmetic sequence is $$-287$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$267$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is given that $$a_71 = -277$$ and $$d = 10$$.<br>\r\nWe can get the previous term in an arithmetic sequence by subtracting the common difference from its next term.<br>\r\n$$a_70 = a_71\\\\;-d$$<br>\r\n$$a_70 = -277\\\\;-\\\\;(10) = -287$$<br>\r\nSo, the 70th term of the given arithmetic sequence is $$-287$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$327$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is given that $$a_71 = -277$$ and $$d = 10$$.<br>\r\nWe can get the previous term in an arithmetic sequence by subtracting the common difference from its next term.<br>\r\n$$a_70 = a_71\\\\;-d$$<br>\r\n$$a_70 = -277\\\\;-\\\\;(10) = -287$$<br>\r\nSo, the 70th term of the given arithmetic sequence is $$-287$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-287$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"It is given that $$a_71 = -277$$ and $$d = 10$$.<br>\r\nWe can get the previous term in an arithmetic sequence by subtracting the common difference from its next term.<br>\r\n$$a_70 = a_71\\\\;-d$$<br>\r\n$$a_70 = -277\\\\;-\\\\;(10) = -287$$<br>\r\nSo, the 70th term of the given arithmetic sequence is $$-287$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"It is given that $$a_71 = -277$$ and $$d = 10$$.<br>\r\nWe can get the previous term in an arithmetic sequence by subtracting the common difference from its next term.<br>\r\n$$a_70 = a_71\\\\;-d$$<br>\r\n$$a_70 = -277\\\\;-\\\\;(10) = -287$$<br>\r\nSo, the 70th term of the given arithmetic sequence is $$-287$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-common-difference\">Frequently Asked Questions on Common Difference<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-05a6e6eb-4438-447f-84b9-e0e58a6e497a\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-05a6e6eb-4438-447f-84b9-e0e58a6e497a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-05a6e6eb-4438-447f-84b9-e0e58a6e497a\"><strong>Is the common difference the same for all arithmetic sequences?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-05a6e6eb-4438-447f-84b9-e0e58a6e497a\">\n\n<p class=\"eplus-wrapper\">No, all arithmetic sequences do not have the same common difference. But the common difference for an arithmetic sequence is always constant.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-05a6e6eb-4438-447f-84b9-e0e58a6e497a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-05a6e6eb-4438-447f-84b9-e0e58a6e497a\"><strong>Can the common difference for an arithmetic sequence be different?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-05a6e6eb-4438-447f-84b9-e0e58a6e497a\">\n\n<p class=\"eplus-wrapper\">No, the common difference for an arithmetic sequence is always constant. If the common difference is not constant in a sequence then it is not an arithmetic sequence.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-05a6e6eb-4438-447f-84b9-e0e58a6e497a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-05a6e6eb-4438-447f-84b9-e0e58a6e497a\"><strong>What are some common difference examples?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-05a6e6eb-4438-447f-84b9-e0e58a6e497a\">\n\n<p class=\"eplus-wrapper\">Some common difference examples are:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For the arithmetic sequence {0, 2, 4, 6, 8, 10, 12}, the common difference is 2.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For the arithmetic sequence {4, 7, 10, 13, &#8230;}, the common difference is 3.&nbsp;For the arithmetic sequence {60, 55, 50, 45, 40, &#8230;}, the common difference is $-5$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-05a6e6eb-4438-447f-84b9-e0e58a6e497a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-05a6e6eb-4438-447f-84b9-e0e58a6e497a\"><strong>Can the common difference for an arithmetic sequence be a decimal or a fraction?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-05a6e6eb-4438-447f-84b9-e0e58a6e497a\">\n\n<p class=\"eplus-wrapper\">Yes, the common difference for an arithmetic sequence can be a decimal or a fraction. It can be any rational number.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-05a6e6eb-4438-447f-84b9-e0e58a6e497a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-05a6e6eb-4438-447f-84b9-e0e58a6e497a\"><strong>Which letter represents the common difference of an arithmetic sequence?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-05a6e6eb-4438-447f-84b9-e0e58a6e497a\">\n\n<p class=\"eplus-wrapper\">The letter \u201cd\u201d represents the common difference of an arithmetic sequence.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-05a6e6eb-4438-447f-84b9-e0e58a6e497a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-05a6e6eb-4438-447f-84b9-e0e58a6e497a\"><strong>Can the common difference be negative?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-05a6e6eb-4438-447f-84b9-e0e58a6e497a\">\n\n<p class=\"eplus-wrapper\">Yes. Common differences can also be negative.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $6,\\; 4,\\; 2,\\; 0,\\; -2,\\; -4,\\&#8217; -6,$ \u2026Here, the common difference is $-2$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is the Common Difference of an Arithmetic Sequence? An arithmetic sequence is a sequence of numbers in which the difference between two consecutive numbers is always constant. This difference is called a common difference of the arithmetic sequence. For example, 1, 3, 5, 7, 9, \u2026 is an arithmetic sequence. Here, the difference between &#8230; <a title=\"Common Difference: Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference\" aria-label=\"More on Common Difference: Definition with Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26536","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26536","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=26536"}],"version-history":[{"count":14,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26536\/revisions"}],"predecessor-version":[{"id":40963,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26536\/revisions\/40963"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}