{"id":138,"date":"2022-04-13T10:06:58","date_gmt":"2022-04-13T10:06:58","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=138"},"modified":"2025-03-05T11:48:22","modified_gmt":"2025-03-05T11:48:22","slug":"g-4-partial-sums-of-arithmetic-series","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/g-4-partial-sums-of-arithmetic-series\/","title":{"rendered":"G.4 Partial sums of arithmetic series"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Partial sums of arithmetic series<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9eab8b80198ef55bc96d653fd9da2182\" style=\"color:#74008b;text-transform:uppercase\"><strong>key notes:<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">A&nbsp;<strong>sequence<\/strong>&nbsp;is an ordered list of numbers. This list can have a finite number of terms or infinitely many&nbsp;terms.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">A&nbsp;<strong>series<\/strong>&nbsp;is the sum of a sequence of&nbsp;numbers.<\/li>\n\n\n\n<li class=\"has-large-font-size\">The&nbsp;nth<strong>&nbsp;partial sum&nbsp;<\/strong>(S<sub>n<\/sub>)&nbsp;of a series is the sum of its first&nbsp;n&nbsp;terms.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">A&nbsp;<strong>sequence<\/strong>&nbsp;is an ordered list of numbers. This list can have a finite number of terms or infinitely many&nbsp;terms.<\/p>\n\n\n\n<p class=\"has-large-font-size\">A&nbsp;<strong>series<\/strong>&nbsp;is the sum of a sequence of&nbsp;numbers.<\/p>\n\n\n\n<p class=\"has-large-font-size\">The&nbsp;nth<strong>&nbsp;partial sum&nbsp;<\/strong>(S<sub>n<\/sub>)&nbsp;of a series is the sum of its first&nbsp;n&nbsp;terms.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-b3fd92edf249d6bd67c80d150b25cc86\" style=\"background-color:#abbbf0\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\ud83d\udd14 Find&nbsp;the third partial sum of the&nbsp;series.<\/p>\n\n\n\n<p>5 + 8 + 11 + 14 + 17 + 20 + \u22ef<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d98834d66a39c1904867f2d7bc52ce99\" style=\"color:#b00012\">Write&nbsp;your answer as an integer or a fraction in simplest&nbsp;form.<\/p>\n\n\n\n<p>S<sub>3<\/sub>=____<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the&nbsp;series.<\/p>\n\n\n\n<p>5 + 8 + 11 + 14 + 17 + 20 + \u22ef<\/p>\n\n\n\n<p>The&nbsp;third partial sum,&nbsp;S<sub>3<\/sub>,&nbsp;is the sum of the first three&nbsp;terms.<\/p>\n\n\n\n<p>S<sub>3<\/sub> = 5 + 8 + 11 = 24<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-6fa496f0fe59d960fdab7bfec6108eab\" style=\"background-color:#f0a4a4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\ud83d\udd14 Find&nbsp;the third partial sum of the&nbsp;series.<\/p>\n\n\n\n<p>8 + 11 + 14 + 17 + 20 + 23 + \u22ef<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d98834d66a39c1904867f2d7bc52ce99\" style=\"color:#b00012\">Write&nbsp;your answer as an integer or a fraction in simplest&nbsp;form.<\/p>\n\n\n\n<p>S<sub>3<\/sub>=<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the&nbsp;series.<\/p>\n\n\n\n<p>8 + 11 + 14 + 17 + 20 + 23 + \u22ef<\/p>\n\n\n\n<p>The&nbsp;third partial sum,&nbsp;S<sub>3<\/sub>,&nbsp;is the sum of the first three&nbsp;terms.<\/p>\n\n\n\n<p>S<sub>3<\/sub>= 8 + 11 + 14 = 33<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-60000d3519fc81d8bee52f1d8c729969\" style=\"background-color:#aeeea9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-936793d9d05861160ddbe998bddbc465\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\ud83d\udd14 Find&nbsp;the third partial sum of the&nbsp;series.<\/p>\n\n\n\n<p>4 + 11 + 18 + 25 + 32 + 39 + \u22ef<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d98834d66a39c1904867f2d7bc52ce99\" style=\"color:#b00012\">Write&nbsp;your answer as an integer or a fraction in simplest&nbsp;form.<\/p>\n\n\n\n<p>S<sub>3<\/sub>=<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the&nbsp;series.<\/p>\n\n\n\n<p>4 + 11 + 18 + 25 + 32 + 39 + \u22ef<\/p>\n\n\n\n<p>The&nbsp;third partial sum,&nbsp;S3,&nbsp;is the sum of the first three&nbsp;terms.<\/p>\n\n\n\n<p>S<sub>3<\/sub>= 4 + 11 + 18 = 33<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/79952\/954\/287\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-25.png\" alt=\"\" class=\"wp-image-6795\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-25.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-25-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-25-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/79566\/579\/283\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-43.png\" alt=\"\" class=\"wp-image-6796\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-43.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-43-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-43-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Partial sums of arithmetic series key notes: A&nbsp;sequence&nbsp;is an ordered list of numbers. This list can have a finite number of terms or infinitely many&nbsp;terms. A&nbsp;sequence&nbsp;is an ordered list of numbers. This list can have a finite number of terms or infinitely many&nbsp;terms. A&nbsp;series&nbsp;is the sum of a sequence of&nbsp;numbers. The&nbsp;nth&nbsp;partial sum&nbsp;(Sn)&nbsp;of a series is<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/g-4-partial-sums-of-arithmetic-series\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.4 Partial sums of arithmetic series&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-138","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=138"}],"version-history":[{"count":20,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138\/revisions"}],"predecessor-version":[{"id":17607,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138\/revisions\/17607"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}