{"id":36367,"date":"2023-12-05T16:34:00","date_gmt":"2023-12-05T16:34:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=36367"},"modified":"2023-12-11T04:52:59","modified_gmt":"2023-12-11T04:52:59","slug":"nth-term-of-ap-definition-formula-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/nth-term-of-ap","title":{"rendered":"Nth Term of AP &#8211; Definition, Formula, Examples, FAQs"},"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-81ea4271-74c6-4e99-aa39-e279876e2979\" 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\/nth-term-of-ap#0-what-is-the-n-th-term-of-an-ap>What Is the nth Term of an AP?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/nth-term-of-ap#1-the-n-th-term-of-an-ap-formula>The nth Term of an AP Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/nth-term-of-ap#4-how-to-find-the-n-th-term-of-an-ap>How to Find the nth Term of an AP<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/nth-term-of-ap#7-solved-examples-on-the-n-th-term-of-an-ap>Solved Examples on the nth Term of an AP<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/nth-term-of-ap#8-practice-problems-on-the-n-th-term-of-an-ap>Practice Problems on the nth Term of an AP<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/nth-term-of-ap#9-frequently-asked-questions-about-the-n-th-term-of-an-ap>Frequently Asked Questions about the nth Term of an AP<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-n-th-term-of-an-ap\">What Is the n<sup>th<\/sup> Term of an AP?<\/h2>\n\n\n\n<p><strong>The n<\/strong><strong><sup>th<\/sup><\/strong><strong> term of an AP is the term that occupies the n<\/strong><strong><sup>th<\/sup><\/strong><strong> position from the beginning (left side) of an A.P. sequence. It&#8217;s a way to identify a specific term in the A.P. sequence based on its position.<\/strong><\/p>\n\n\n\n<p>Suppose you have a sequence of numbers that increase by the same amount each time. This kind of <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/arithmetic-patterns\">arithmetic sequence<\/a> is called an <strong>Arithmetic Progression<\/strong> (<strong>AP)<\/strong>.&nbsp;<\/p>\n\n\n\n<p><strong>Example 1<\/strong>: Consider the sequence 2, 5, 8, 11, 14, &#8230;<\/p>\n\n\n\n<p>Here, the first term of this AP is T1 = 2, the second term is T2 = 5, the third term is T3 = 8, and so on. Each number in this series is more than the previous one by 3. Here, 3 is called the &#8220;<a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/common-difference\">common difference<\/a>&#8221; because the same difference between any two consecutive terms is constant.<\/p>\n\n\n\n<p><strong>Example 2<\/strong>: In the given sequence, the first term is -6. The common difference is 7.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"326\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/ap-sequence-example.png\" alt=\"AP sequence example\" class=\"wp-image-36373\" title=\"AP sequence example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/ap-sequence-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/ap-sequence-example-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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\/add-tenths-and-hundredths-using-models\" 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\/decimals_add_tenth_hundredth_models_pt.png\" alt=\"Add Tenths and Hundredths Using Models 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\">Add Tenths and Hundredths Using Models 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\/analyze-and-represent-data-using-bar-graph\" 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\/data_analyze_represent_data_pt.png\" alt=\"Analyze and Represent Data Using Bar Graph 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\">Analyze and Represent Data Using Bar Graph 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\/analyze-data-using-bar-graph\" 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\/data_analyze_data_pt.png\" alt=\"Analyze Data Using Bar Graph 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\">Analyze Data Using Bar Graph 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\/answer-how-many-more-or-less-using-bar-graphs\" 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\/data_less_more_bar_grph_pt.png\" alt=\"Answer How Many More or Less using Bar Graphs 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\">Answer How Many More or Less using Bar Graphs 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\/applications-of-skip-counting\" 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\/count_comp_skip100_application_problem_pt.png\" alt=\"Applications of Skip Counting 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\">Applications of Skip Counting 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\/apply-distributive-property\" 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\/mult_div_facts_mul_dispro_exp1_pt.png\" alt=\"Apply Distributive Property 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\">Apply Distributive Property 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\/apply-skip-counting-in-real-world\" 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\/count_comp_skip10_application_problem_pt.png\" alt=\"Apply Skip Counting in Real World 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\">Apply Skip Counting in Real World 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-fact-related-to-shapes\" 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\/geometry_check_statement_pt.png\" alt=\"Choose the Correct Fact Related to Shapes 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 Fact Related to Shapes 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-number-placed-at-tenths-or-hundredths\" 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\/decimals_identify_digit_at_place_pt.png\" alt=\"Choose the Correct Number Placed at Tenths or Hundredths 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 Number Placed at Tenths or Hundredths 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-unit-of-capacity\" 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_estimate_capacity_2_pt.png\" alt=\"Choose the Correct Unit of Capacity 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 Unit of Capacity 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 = 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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\" id=\"1-the-n-th-term-of-an-ap-formula\">The n<sup>th<\/sup> Term of an AP Formula<\/h2>\n\n\n\n<p>The n<sup>th<\/sup> term of an AP is obtained by adding the common difference (d) multiplied by (n-1) to the first term (a\u200b) of the progression.<\/p>\n\n\n\n<p>The nth term of an arithmetic progression (AP) can be calculated using the following formula:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>Tn= a+(n &#8211; 1)d<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>where:&nbsp;<\/p>\n\n\n\n<p>Tn is the nth term of the AP<\/p>\n\n\n\n<p>a is the first term of the AP<\/p>\n\n\n\n<p>n indicates the position of the term<\/p>\n\n\n\n<p>d is the common difference between consecutive terms of the AP.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"327\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/ap-formula-for-nth-term.png\" alt=\"AP formula for nth term\" class=\"wp-image-36371\" title=\"AP formula for nth term\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/ap-formula-for-nth-term.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/ap-formula-for-nth-term-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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\/add-and-color-shapes-within-10\" 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\" 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class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-color-shapes-within-5\" 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\/add-and-color-shapes-within-5.jpeg\" alt=\"Add and Color Shapes (Within 5)\">\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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-horizontal\" 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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-horizontal.jpeg\" alt=\"Add and Subtract Tenths and Hundredths less than 1 with Regrouping: Horizontal 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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-missing-digits\" 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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-missing-digits.jpeg\" alt=\"Add and Subtract Tenths and Hundredths less than 1 with Regrouping: Missing Digits 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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-missing-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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-missing-numbers.jpeg\" alt=\"Add and Subtract Tenths and Hundredths less than 1 with Regrouping: Missing 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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-vertical\" 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\/add-and-subtract-tenths-and-hundredths-less-than-1-with-regrouping-vertical.jpeg\" alt=\"Add and Subtract Tenths and Hundredths less than 1 with Regrouping: Vertical Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-what-is-the-importance-of-the-n-th-term-of-an-ap-formula\">What Is the Importance of the n<sup>th<\/sup> Term of an AP Formula?<\/h2>\n\n\n\n<p>If you want to find the 6<sup>th<\/sup> number in this sequence without counting all the previous numbers, instead of repeatedly adding 3, you can use the &#8220;n<sup>th<\/sup> term of the AP formula.<\/p>\n\n\n\n<p>It is not practical to keep counting one at a time, especially if we\u2019re searching for a term far down the sequence, like the 25<sup>th<\/sup> term for the 100<sup>th<\/sup> term.&nbsp;<\/p>\n\n\n\n<p>The formula lets us figure out any term in the sequence without having to count all the previous ones. It works by taking the first term and adding the common difference multiplied by (n &#8211; 1). This way, we can jump straight to the term we&#8217;re interested in without doing all the intermediate steps.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-derivation-of-the-n-th-term-of-an-ap\">Derivation of the n<sup>th<\/sup> Term of an AP<\/h2>\n\n\n\n<p>An arithmetic progression (A.P) is a sequence of numbers where each term is obtained by adding a fixed amount, known as the common difference, to the preceding term.<\/p>\n\n\n\n<p>Consider the A.P. given by<\/p>\n\n\n\n<p>a, a+d, a+2d, a+3d,&#8230;<\/p>\n\n\n\n<p>1<sup>st<\/sup> term = T1 = a<\/p>\n\n\n\n<p>2<sup>nd<\/sup> term = T2 = a+d =a+(2-1)d<\/p>\n\n\n\n<p>3<sup>rd<\/sup> term = T3=a+2d=a+(3-1)d<\/p>\n\n\n\n<p>4<sup>th<\/sup> term = T4=a+3d=a+ (4-1)d<\/p>\n\n\n\n<p>.<\/p>\n\n\n\n<p>.<\/p>\n\n\n\n<p>.<\/p>\n\n\n\n<p>n<sup>th<\/sup> term Tn=a+(n-1)d<\/p>\n\n\n\n<p>This formula represents the value of the nth term in AP whose first term is a and the common difference is d.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-how-to-find-the-n-th-term-of-an-ap\">How to Find the n<sup>th<\/sup> Term of an AP<\/h2>\n\n\n\n<p>Let&#8217;s understand the steps to find the n<sup>th<\/sup> term of an Arithmetic Progression (AP) with the help of an example.<\/p>\n\n\n\n<p><strong>Formula<\/strong>: n<sup>th<\/sup> term Tn=a+(n-1)d<\/p>\n\n\n\n<p><strong>Example<\/strong>: Find the 10<sup>th<\/sup> term of the arithmetic progression 3, 8, 13, 18,&#8230;<\/p>\n\n\n\n<p>Here, first term (a1) =&nbsp; 3<\/p>\n\n\n\n<p>common difference (d) = 4<\/p>\n\n\n\n<p>n = 10<\/p>\n\n\n\n<p><strong>Formula:<\/strong> Tn= a + (n &#8211; 1)d<\/p>\n\n\n\n<p>T10=&nbsp; 3+(10-1)4<\/p>\n\n\n\n<p>T10=&nbsp; 3+(10-1)4<\/p>\n\n\n\n<p>T10= 3+(9)4<\/p>\n\n\n\n<p>T10= 3+36&nbsp;<\/p>\n\n\n\n<p>T10 = 39<\/p>\n\n\n\n<p>Thus, the 10<sup>th<\/sup> term of the sequence is 39.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-facts-about-the-n-th-term-of-an-ap-formula\">Facts about the n<sup>th<\/sup> Term of an AP Formula<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The common difference (d) remains constant throughout the entire arithmetic progression. It&#8217;s the fixed amount that each term increases or decreases by.<\/li>\n\n\n\n<li>The first term (a1) of the AP is the value at the first position, i.e., a1=a1+(1-1)d, which simplifies to a1.<\/li>\n\n\n\n<li>The nth term represents the value of the term at the nth position in the sequence. It&#8217;s the term that&#8217;s n steps away from the first term.<\/li>\n\n\n\n<li>The formula works for negative terms as well. If the common difference is negative, adding it will cause the terms to decrease as you move along the sequence.<\/li>\n\n\n\n<li>The formula can also be used to find terms with non-integer values. As long as the common difference and initial term are real numbers, the formula remains valid.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about finding the n<sup>th<\/sup> term of an arithmetic progression (AP). This formula lets you find any term in an arithmetic progression without having to add the common difference again and again. It&#8217;s super useful when you&#8217;re dealing with large sequences and want to find terms quickly! Let&#8217;s solve a few examples and MCQs for effective practice.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved-examples-on-the-n-th-term-of-an-ap\">Solved Examples on the n<sup>th<\/sup> Term of an AP<\/h2>\n\n\n\n<p><strong>Example 1: Find the 10<\/strong><strong><sup>th<\/sup><\/strong><strong> term of the arithmetic progression: 5, 9, 13, 17, \u2026<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>First term (a1) =&nbsp; 5<\/p>\n\n\n\n<p>common difference (d) = 4<\/p>\n\n\n\n<p>n = 10<\/p>\n\n\n\n<p>Tn = a + (n &#8211; 1)d<\/p>\n\n\n\n<p>T10=&nbsp; 5+(10-1)4<\/p>\n\n\n\n<p>T10= 5+(9)4<\/p>\n\n\n\n<p>T10= 5+36 = 41<\/p>\n\n\n\n<p>Thus, the 10th term of the sequence is 41.<\/p>\n\n\n\n<p><strong>Example 2: Find the 15<\/strong><strong><sup>th<\/sup><\/strong><strong> term of the arithmetic progression: 2, 7, 12, 17, \u2026<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>First term (a1) =&nbsp; 2<\/p>\n\n\n\n<p>common difference (d) = 5<\/p>\n\n\n\n<p>n = 15<\/p>\n\n\n\n<p>Tn= a + (n &#8211; 1)d<\/p>\n\n\n\n<p>T15=&nbsp; 2+(15-1)5<\/p>\n\n\n\n<p>T15= 2+(14)5<\/p>\n\n\n\n<p>T15= 2+70 = 72<\/p>\n\n\n\n<p>Thus, the 15<sup>th<\/sup> term of the sequence is 72.<\/p>\n\n\n\n<p><strong>Example 3: What is the position of 120 in the given AP?<\/strong><\/p>\n\n\n\n<p><strong>5, 10, 15, 20,\u2026,120,&#8230;<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>First term = a = 5&nbsp;<\/p>\n\n\n\n<p>Common difference (d) = 5.<\/p>\n\n\n\n<p>Tn = 120<\/p>\n\n\n\n<p>We will find the value of n.<\/p>\n\n\n\n<p>Tn= a + (n &#8211; 1)d<\/p>\n\n\n\n<p>120 = 5 + (n &#8211; 1) 5&nbsp;<\/p>\n\n\n\n<p>120 = 5 + 5n &#8211; 5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>120 = 5n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>&nbsp;n = 1205&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>&nbsp;n = 24<\/p>\n\n\n\n<p>120 is the 24<sup>th<\/sup> term of the given AP.<\/p>\n\n\n\n<p><strong>Example 4: Find the 15<\/strong><strong><sup>th<\/sup><\/strong><strong> term of an AP whose 8<\/strong><strong><sup>th<\/sup><\/strong><strong> term is 27 and the common difference is 4.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>T8 = 27<\/p>\n\n\n\n<p>d = 4<\/p>\n\n\n\n<p>Formula: Tn = a + (n &#8211; 1)d<\/p>\n\n\n\n<p>T8 = a + (8 &#8211; 1)(4)<\/p>\n\n\n\n<p>27 = a + 28<\/p>\n\n\n\n<p>a = 27-28<\/p>\n\n\n\n<p>a = -1<\/p>\n\n\n\n<p>Let\u2019s find the 15<sup>th<\/sup> term.<\/p>\n\n\n\n<p>T15 = a + (15 &#8211; 1) d<\/p>\n\n\n\n<p>T15 = -1 + (14) 4&nbsp;&nbsp;<\/p>\n\n\n\n<p>T15 = &nbsp; -1+56&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>T15 = 55<\/p>\n\n\n\n<p>Thus, the 15<sup>th<\/sup> term of the AP is 55<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-the-n-th-term-of-an-ap\">Practice Problems on the n<sup>th<\/sup> Term of an AP<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Nth Term of AP - Definition, Formula, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the formula for the nth term of an arithmetic progression (AP)?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$T_{n} = a_{1} + (n - 1)d$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$T_{n} = a_{1} + (n + 1)d$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$T_{n} = a_{1} + nd$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$T_{n} = a_{1} - (n - 1)d$<\/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: $T_{n} = a_{1} + (n - 1)d$<br\/>The nth term of an arithmetic progression (AP) can be calculated using the formula$T_{n} = a1 + (n - 1)d$, where $a_{1}$ is the first term, d is the common difference, and n is the term number.<\/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\">What does n represent in the nth term formula of an AP?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">The value of the nth term in the sequence<\/div><div class=\"spq_answer_block\" data-value=\"1\">The total number of terms in the sequence<\/div><div class=\"spq_answer_block\" data-value=\"2\">The position of the term in the sequence<\/div><div class=\"spq_answer_block\" data-value=\"3\">The common difference of the sequence<\/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: The position of the term in the sequence<br\/>n represents the position of the term in the sequence. It helps determine which term's value is being calculated using the formula.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the nth term of an AP if the first term is 12 and the common difference is 0?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$T_{n} = 12$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$T_{n} = 12n$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$T_{n} = 0$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$T_{n} = n$<\/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: $T_{n} = 12$<br\/>When the common difference is 0, it means that the terms in the sequence are all the same. In this case, the nth term formula simplifies to $T_{n} = a = 12$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What information is NOT required to determine the nth term of an arithmetic progression (AP)?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">The first term<\/div><div class=\"spq_answer_block\" data-value=\"1\">The term number (position)<\/div><div class=\"spq_answer_block\" data-value=\"2\">The common difference.<\/div><div class=\"spq_answer_block\" data-value=\"3\">The last term<\/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: The last term<br\/>To determine the nth term of an AP, you need the value of the first term, the common difference, and the term number (position). The value of the last term is not necessary to calculate the nth term.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">If a = 10 and d = 10, then the first four terms will be:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10, 30, 50, 60<\/div><div class=\"spq_answer_block\" data-value=\"1\">10, 20, 30, 40<\/div><div class=\"spq_answer_block\" data-value=\"2\">10, 15, 20, 25<\/div><div class=\"spq_answer_block\" data-value=\"3\">10, 18, 20, 30<\/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: 10, 20, 30, 40<br\/>$a = 10, d = 10, a_{1} = a = 10$<br>\r\n$a_{2} = a_{1} + d = 10 + 10 = 20$<br>\r\n$a_{3} = a_{2} + d = 20 + 10 = 30$<br>\r\n$a_{4} = a_{3} + d = 30+10 = 40$<\/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\": \"Nth Term of AP - Definition, Formula, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Nth Term of AP\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the formula for the nth term of an arithmetic progression (AP)?\",\n                    \"text\": \"What is the formula for the nth term of an arithmetic progression (AP)?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The nth term of an arithmetic progression (AP) can be calculated using the formula$$T_{n} = a1 + (n - 1)d$$, where $$a_{1}$$ is the first term, d is the common difference, and n is the term number.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$T_{n} = a_{1} + (n + 1)d$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The nth term of an arithmetic progression (AP) can be calculated using the formula$$T_{n} = a1 + (n - 1)d$$, where $$a_{1}$$ is the first term, d is the common difference, and n is the term number.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$T_{n} = a_{1} + nd$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The nth term of an arithmetic progression (AP) can be calculated using the formula$$T_{n} = a1 + (n - 1)d$$, where $$a_{1}$$ is the first term, d is the common difference, and n is the term number.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$T_{n} = a_{1} - (n - 1)d$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The nth term of an arithmetic progression (AP) can be calculated using the formula$$T_{n} = a1 + (n - 1)d$$, where $$a_{1}$$ is the first term, d is the common difference, and n is the term number.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$T_{n} = a_{1} + (n - 1)d$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The nth term of an arithmetic progression (AP) can be calculated using the formula$$T_{n} = a1 + (n - 1)d$$, where $$a_{1}$$ is the first term, d is the common difference, and n is the term number.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The nth term of an arithmetic progression (AP) can be calculated using the formula$$T_{n} = a1 + (n - 1)d$$, where $$a_{1}$$ is the first term, d is the common difference, and n is the term number.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What does n represent in the nth term formula of an AP?\",\n                    \"text\": \"What does n represent in the nth term formula of an AP?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"n represents the position of the term in the sequence. It helps determine which term's value is being calculated using the formula.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The value of the nth term in the sequence\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"n represents the position of the term in the sequence. It helps determine which term's value is being calculated using the formula.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The total number of terms in the sequence\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"n represents the position of the term in the sequence. It helps determine which term's value is being calculated using the formula.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The common difference of the sequence\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"n represents the position of the term in the sequence. It helps determine which term's value is being calculated using the formula.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"The position of the term in the sequence\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"n represents the position of the term in the sequence. It helps determine which term's value is being calculated using the formula.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"n represents the position of the term in the sequence. It helps determine which term's value is being calculated using the formula.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the nth term of an AP if the first term is 12 and the common difference is 0?\",\n                    \"text\": \"What is the nth term of an AP if the first term is 12 and the common difference is 0?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"When the common difference is 0, it means that the terms in the sequence are all the same. In this case, the nth term formula simplifies to $$T_{n} = a = 12$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$T_{n} = 12n$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"When the common difference is 0, it means that the terms in the sequence are all the same. In this case, the nth term formula simplifies to $$T_{n} = a = 12$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$T_{n} = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"When the common difference is 0, it means that the terms in the sequence are all the same. In this case, the nth term formula simplifies to $$T_{n} = a = 12$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$T_{n} = n$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"When the common difference is 0, it means that the terms in the sequence are all the same. In this case, the nth term formula simplifies to $$T_{n} = a = 12$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$T_{n} = 12$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"When the common difference is 0, it means that the terms in the sequence are all the same. In this case, the nth term formula simplifies to $$T_{n} = a = 12$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"When the common difference is 0, it means that the terms in the sequence are all the same. In this case, the nth term formula simplifies to $$T_{n} = a = 12$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What information is NOT required to determine the nth term of an arithmetic progression (AP)?\",\n                    \"text\": \"What information is NOT required to determine the nth term of an arithmetic progression (AP)?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"To determine the nth term of an AP, you need the value of the first term, the common difference, and the term number (position). The value of the last term is not necessary to calculate the nth term.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The first term\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To determine the nth term of an AP, you need the value of the first term, the common difference, and the term number (position). The value of the last term is not necessary to calculate the nth term.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The term number (position)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To determine the nth term of an AP, you need the value of the first term, the common difference, and the term number (position). The value of the last term is not necessary to calculate the nth term.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The common difference.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To determine the nth term of an AP, you need the value of the first term, the common difference, and the term number (position). The value of the last term is not necessary to calculate the nth term.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"The last term\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"To determine the nth term of an AP, you need the value of the first term, the common difference, and the term number (position). The value of the last term is not necessary to calculate the nth term.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"To determine the nth term of an AP, you need the value of the first term, the common difference, and the term number (position). The value of the last term is not necessary to calculate the nth term.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If a = 10 and d = 10, then the first four terms will be:\",\n                    \"text\": \"If a = 10 and d = 10, then the first four terms will be:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$a = 10, d = 10, a_{1} = a = 10$$<br>\r\n$$a_{2} = a_{1} + d = 10 + 10 = 20$$<br>\r\n$$a_{3} = a_{2} + d = 20 + 10 = 30$$<br>\r\n$$a_{4} = a_{3} + d = 30+10 = 40$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10, 30, 50, 60\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$a = 10, d = 10, a_{1} = a = 10$$<br>\r\n$$a_{2} = a_{1} + d = 10 + 10 = 20$$<br>\r\n$$a_{3} = a_{2} + d = 20 + 10 = 30$$<br>\r\n$$a_{4} = a_{3} + d = 30+10 = 40$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10, 15, 20, 25\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$a = 10, d = 10, a_{1} = a = 10$$<br>\r\n$$a_{2} = a_{1} + d = 10 + 10 = 20$$<br>\r\n$$a_{3} = a_{2} + d = 20 + 10 = 30$$<br>\r\n$$a_{4} = a_{3} + d = 30+10 = 40$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10, 18, 20, 30\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$a = 10, d = 10, a_{1} = a = 10$$<br>\r\n$$a_{2} = a_{1} + d = 10 + 10 = 20$$<br>\r\n$$a_{3} = a_{2} + d = 20 + 10 = 30$$<br>\r\n$$a_{4} = a_{3} + d = 30+10 = 40$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"10, 20, 30, 40\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$a = 10, d = 10, a_{1} = a = 10$$<br>\r\n$$a_{2} = a_{1} + d = 10 + 10 = 20$$<br>\r\n$$a_{3} = a_{2} + d = 20 + 10 = 30$$<br>\r\n$$a_{4} = a_{3} + d = 30+10 = 40$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$a = 10, d = 10, a_{1} = a = 10$$<br>\r\n$$a_{2} = a_{1} + d = 10 + 10 = 20$$<br>\r\n$$a_{3} = a_{2} + d = 20 + 10 = 30$$<br>\r\n$$a_{4} = a_{3} + d = 30+10 = 40$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-about-the-n-th-term-of-an-ap\">Frequently Asked Questions about the n<sup>th<\/sup> Term of an AP<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-561c210e-7cb5-4319-898c-fb2e96eaa460\" 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-0-561c210e-7cb5-4319-898c-fb2e96eaa460\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-561c210e-7cb5-4319-898c-fb2e96eaa460\"><strong>What is the n<sup>th<\/sup> term of an arithmetic progression?<\/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-0-561c210e-7cb5-4319-898c-fb2e96eaa460\">\n\n<p>The n<sup>th<\/sup> term of an arithmetic progression is the value of the term that occupies the nth position in the 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-1-561c210e-7cb5-4319-898c-fb2e96eaa460\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-561c210e-7cb5-4319-898c-fb2e96eaa460\"><strong>Can the n<sup>th<\/sup> term of an AP be a negative number?<\/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-1-561c210e-7cb5-4319-898c-fb2e96eaa460\">\n\n<p>Yes, the nth term can be a negative number if the common difference (d) is negative. The formula accounts for both positive and negative terms.<\/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-2-561c210e-7cb5-4319-898c-fb2e96eaa460\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-561c210e-7cb5-4319-898c-fb2e96eaa460\"><strong>Do I always need to know the previous terms to find the n<sup>th<\/sup> term in an AP?<\/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-2-561c210e-7cb5-4319-898c-fb2e96eaa460\">\n\n<p>No, you don&#8217;t need to know the previous terms to find the nth term using the formula. The formula directly calculates the term at a specific position based on the first term and the common difference.<\/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-3-561c210e-7cb5-4319-898c-fb2e96eaa460\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-561c210e-7cb5-4319-898c-fb2e96eaa460\"><strong>Can I use the n<sup>th<\/sup> term formula for non-integer terms?<\/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-3-561c210e-7cb5-4319-898c-fb2e96eaa460\">\n\n<p>Yes, the n<sup>th<\/sup> term formula is applicable for both integer and non-integer terms. As long as the first term and the common difference are real numbers, the formula remains valid.<\/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-4-561c210e-7cb5-4319-898c-fb2e96eaa460\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-561c210e-7cb5-4319-898c-fb2e96eaa460\"><strong>Is the n<sup>th<\/sup> term formula the same for all arithmetic progressions?<\/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-4-561c210e-7cb5-4319-898c-fb2e96eaa460\">\n\n<p>Yes, the formula&nbsp; Tn= a1 + (n &#8211; 1)d \u200b is applicable to all arithmetic progressions, regardless of the values of the first term and common difference. It&#8217;s a universal formula.<\/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-5-561c210e-7cb5-4319-898c-fb2e96eaa460\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-561c210e-7cb5-4319-898c-fb2e96eaa460\"><strong>Is the n<sup>th<\/sup> term formula used only in mathematics?<\/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-5-561c210e-7cb5-4319-898c-fb2e96eaa460\">\n\n<p>No, the concept of the nth term and the formula have practical applications in various fields, including physics, finance, computer science, and more. It helps model situations where values change in a consistent manner.<\/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-6-561c210e-7cb5-4319-898c-fb2e96eaa460\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-561c210e-7cb5-4319-898c-fb2e96eaa460\"><strong>How do you find the value of n in AP?<\/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-6-561c210e-7cb5-4319-898c-fb2e96eaa460\">\n\n<p>To determine the nth term of an arithmetic progression (AP), start by identifying the first term as &#8220;a&#8221; and the common difference as &#8220;d.&#8221; Decide on the term number, &#8220;n,&#8221; for which you want to find the value. Then, use the formula,&nbsp; Tn= a1 + (n &#8211; 1)d, where \u200bTn represents the nth term, &#8220;a&#8221; is the first term, &#8220;d&#8221; is the common difference, and here&nbsp; &#8220;n&#8221; is the term number.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the nth Term of an AP? The nth term of an AP is the term that occupies the nth position from the beginning (left side) of an A.P. sequence. It&#8217;s a way to identify a specific term in the A.P. sequence based on its position. Suppose you have a sequence of numbers that &#8230; <a title=\"Nth Term of AP &#8211; Definition, Formula, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/nth-term-of-ap\" aria-label=\"More on Nth Term of AP &#8211; Definition, Formula, Examples, FAQs\">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-36367","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\/36367","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=36367"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36367\/revisions"}],"predecessor-version":[{"id":36381,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36367\/revisions\/36381"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=36367"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=36367"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=36367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}