{"id":669,"date":"2012-02-02T21:16:49","date_gmt":"2012-02-02T21:16:49","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=669"},"modified":"2014-12-02T08:33:49","modified_gmt":"2014-12-02T08:33:49","slug":"review-of-arithmetic-series","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/review-of-arithmetic-series\/","title":{"rendered":"Review of Arithmetic Series"},"content":{"rendered":"

An arithmetic sequence is a sequence in which the difference between consecutive terms is constant. A series is the indicated sum of all the terms in a sequence. An arithmetic series is the sum of an arithmetic sequence. Such as,<\/p>\n

2 + 4 + 6 + 8 + 10<\/p>\n

Since the difference is common to all consecutive pairs of terms, it is called the common difference, denoted by d.<\/p>\n

d = an+1<\/sub> – an<\/sub><\/p>\n

An arithmetic series a1<\/sub> + a2<\/sub> + a3<\/sub>+ a4 <\/sub>+\u2026\u2026 + an<\/sub> can be expressed in the terms of first term a1<\/sub> and the common difference d as below.<\/p>\n

Sn<\/sub> = a1<\/sub> + (a1<\/sub> + d) + (a1<\/sub> + 2d) + (a1<\/sub> + 3d) +\u2026..+ (a1<\/sub> + (n \u2013 1)d)<\/p>\n

Sum of n terms of an arithmetic series is give as<\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

General term of a an arithmetic series is as<\/p>\n

an<\/sub> = a1<\/sub> + (n \u2013 1)d<\/p>\n

Example:<\/p>\n

2, 5, 8, 11, 14, 17, 20<\/p>\n

a1<\/sub> = 2<\/p>\n

d = 5 \u2013 2 = 3<\/p>\n

n = 7<\/p>\n

Sum, S7<\/sub> = 7\/2 \u00d7 [2 \u00d72 + (7 \u2013 1)3]\n

= 7\/2 \u00d7 (4 + 6 \u00d7 3)<\/p>\n

= 7\/2 \u00d7 22<\/p>\n

= 7 \u00d7 11 = 77<\/p>\n

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students, visit: SchoolTutoring Academy<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

An arithmetic sequence is a sequence in which the difference between consecutive terms is constant. A series is the indicated sum of all the terms in a sequence. An arithmetic series is the sum of an arithmetic sequence. Such as, 2 + 4 + 6 + 8 + 10 Since the difference is common to […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[138,322,724,1776],"class_list":["post-669","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-arithmeticseries","tag-commondifference","tag-generaltermofarithmeticseries","tag-sumofarithmeticseries"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=669"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/669\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}