{"id":2386,"date":"2022-04-30T17:00:49","date_gmt":"2022-04-30T17:00:49","guid":{"rendered":"https:\/\/swatilathia.com\/?page_id=2386"},"modified":"2022-04-30T17:13:12","modified_gmt":"2022-04-30T17:13:12","slug":"sum-of-n-terms-of-an-a-p","status":"publish","type":"page","link":"https:\/\/swatilathia.com\/?page_id=2386","title":{"rendered":"Sum of n terms of an A.P."},"content":{"rendered":"<body>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69dd87f0ede2e\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69dd87f0ede2e\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#Equation_Sum_of_n_terms_Sn_n2_2a_n-1_d\" >Equation : Sum of n terms | Sn = n\/2 [ 2a + (n-1) d ]<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#Obtain_the_sum_of_the_n_terms_of_following_series_72706866%E2%80%A6\" >Obtain the sum of the n terms of following series :  72+70+68+66+\u2026<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#Obtain_the_sum_of_the_following_sequence\" >Obtain the sum of the following sequence :<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#1_2_4_6_8_10_%E2%80%A6_up_to_12_terms_2_-8_-6_-4_-2_%E2%80%A6_up_to_50_terms_3_1_5_9_13_17_%E2%80%A6_up_to_30_terms_4_4_8_12_16_20_%E2%80%A6_up_to_25_terms\" >(1) 2, 4, 6, 8, 10, \u2026 up to 12 terms (2) -8, -6, -4, -2, \u2026 up to 50 terms (3) 1, 5, 9, 13, 17, \u2026 up to 30 terms (4) 4, 8, 12, 16, 20, \u2026 up to 25 terms<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#For_the_series_10_912_9_%E2%80%A612_find_number_of_terms_%E2%80%93_n_and_T17\" >For the series 10 + 9(1\/2) + 9 +\u2026+1\/2, find number of terms \u2013 n and T17.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#The_sum_of_6_terms_of_an_AP_is_57_and_the_sum_of_its_10_terms_is_155_Find_20th_term\" >The sum of 6 terms of an A.P. is 57, and the sum of its 10 terms is 155. Find 20th term.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#How_many_terms_of_the_series_939087%E2%80%A6_amount_to_975_Find_the_last_term\" >How many terms of the series 93+90+87+\u2026 amount to 975? Find the last term.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#Obtain_the_sum_of_first_n_natural_numbers_and_hence_find_the_sum_of_first_50_numbers\" >Obtain the sum of first n natural numbers and hence find the sum of first 50 numbers.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#The_Sum_of_n_terms_of_an_AP_is_3n2_n_Determine_the_nth_term_and_also_find_10th_term_of_an_AP\" >The Sum of n terms of an A.P. is 3n2 + n. Determine the nth term and also find 10th term of an A.P.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#Find_the_last_term_and_sum_of_the_series\" >Find the last term and sum of the series.<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#ab_ab_a3b_ab_a5b_ab_%E2%80%A6_up_to_15_terms\" >(a+b) \/ (a+b) , (a+3b) \/ (a+b) , (a+5b) \/ (a+b) + \u2026 up to 15 terms<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#How_to_assume_unknown_terms_of_an_AP\" >How to assume unknown terms of an A.P.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#The_sum_of_three_consecutive_terms_in_AP_is_18_and_their_product_is_192_Find_the_three_terms\" >The sum of three consecutive terms in A.P. is 18 and their product is 192. Find the three terms.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/swatilathia.com\/?page_id=2386\/#The_sum_of_four_numbers_in_an_AP_is_24_and_their_product_is_945_Find_the_four_numbers\" >The sum of four numbers in an A.P. is 24 and their product is 945. Find the four numbers.<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Equation_Sum_of_n_terms_Sn_n2_2a_n-1_d\"><\/span>Equation : Sum of n terms | Sn = n\/2 [ 2a + (n-1) d ]<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Equation of Sum of n terms of an Arithmetic Progression\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/wKzIuOtyHsc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Obtain_the_sum_of_the_n_terms_of_following_series_72706866%E2%80%A6\"><\/span>Obtain the sum of the n terms of following series :  72+70+68+66+\u2026 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Obtain_the_sum_of_the_following_sequence\"><\/span>Obtain the sum of the following sequence : <span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"1_2_4_6_8_10_%E2%80%A6_up_to_12_terms_2_-8_-6_-4_-2_%E2%80%A6_up_to_50_terms_3_1_5_9_13_17_%E2%80%A6_up_to_30_terms_4_4_8_12_16_20_%E2%80%A6_up_to_25_terms\"><\/span>(1) 2, 4, 6, 8, 10, \u2026 up to 12 terms (2) -8, -6, -4, -2, \u2026 up to 50 terms (3) 1, 5, 9, 13, 17, \u2026 up to 30 terms (4) 4, 8, 12, 16, 20, \u2026 up to 25 terms<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Sum of n terms of an AP | Examples Part 1\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/jFW3cc7QkzI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"For_the_series_10_912_9_%E2%80%A612_find_number_of_terms_%E2%80%93_n_and_T17\"><\/span>For the series 10 + 9(1\/2) + 9 +\u2026+1\/2, find number of terms \u2013 n and T<sub>17<\/sub>. <span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"The_sum_of_6_terms_of_an_AP_is_57_and_the_sum_of_its_10_terms_is_155_Find_20th_term\"><\/span>The sum of 6 terms of an A.P. is 57, and the sum of its 10 terms is 155. Find 20<sup>th<\/sup> term.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Sum of n terms of an AP | Examples Part 2\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/8b5fj9EglT4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"How_many_terms_of_the_series_939087%E2%80%A6_amount_to_975_Find_the_last_term\"><\/span>How many terms of the series 93+90+87+\u2026 amount to 975? Find the last term.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Sum of n terms | Examples Part 3\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/aLBJq5Zy4l8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Obtain_the_sum_of_first_n_natural_numbers_and_hence_find_the_sum_of_first_50_numbers\"><\/span>Obtain the sum of first n natural numbers and hence find the sum of first 50 numbers. <span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"The_Sum_of_n_terms_of_an_AP_is_3n2_n_Determine_the_nth_term_and_also_find_10th_term_of_an_AP\"><\/span>The Sum of n terms of an A.P. is 3n<sup>2<\/sup> + n. Determine the n<sup>th<\/sup> term and also find 10<sup>th<\/sup> term of an A.P.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Sum of n terms | Example no 19\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/Tlh6sT9OSUo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Find_the_last_term_and_sum_of_the_series\"><\/span>Find the last term and sum of the series.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ab_ab_a3b_ab_a5b_ab_%E2%80%A6_up_to_15_terms\"><\/span>(a+b) \/ (a+b) , (a+3b) \/ (a+b) , (a+5b) \/ (a+b) + \u2026 up to 15 terms<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Sum of n terms of an AP | Example No 22\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/5xw3-vAyx-I?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"How_to_assume_unknown_terms_of_an_AP\"><\/span>How to assume unknown terms of an A.P.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"The_sum_of_three_consecutive_terms_in_AP_is_18_and_their_product_is_192_Find_the_three_terms\"><\/span>The sum of three consecutive terms in A.P. is 18 and their product is 192. Find the three terms.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Find unknown terms of an AP | Example No 23\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/jl44niOxzQc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"The_sum_of_four_numbers_in_an_AP_is_24_and_their_product_is_945_Find_the_four_numbers\"><\/span>The sum of four numbers in an A.P. is 24 and their product is 945. Find the four numbers.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Arithmetic Progression | Example 25 | Find four unknown numbers of an AP\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/Cl5yxOpYZJE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<p><\/p>\n<\/body>","protected":false},"excerpt":{"rendered":"<p>Equation : Sum of n terms | Sn = n\/2 [ 2a + (n-1) d ] Obtain the sum of the n terms of following series : 72+70+68+66+\u2026 Obtain the sum of the following sequence : (1) 2, 4, 6, 8, 10, \u2026 up to 12 terms (2) -8, -6, -4, -2, \u2026 up to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-2386","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2386","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2386"}],"version-history":[{"count":3,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2386\/revisions"}],"predecessor-version":[{"id":2391,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2386\/revisions\/2391"}],"wp:attachment":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}