{"id":134823,"date":"2023-03-21T16:39:39","date_gmt":"2023-03-21T11:09:39","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=134823"},"modified":"2023-03-21T16:39:39","modified_gmt":"2023-03-21T11:09:39","slug":"find-the-sum-of-first-51-terms-of-an-a-p-whose-second-and-third-terms-are-14-and-18-respectively","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/find-the-sum-of-first-51-terms-of-an-a-p-whose-second-and-third-terms-are-14-and-18-respectively","title":{"rendered":"Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18, respectively."},"content":{"rendered":"<h2>Question :Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18, respectively.<\/h2>\n<h3>The correct answer :Let the first term of the AP be a and the common difference be d. Then, the second term is a + d, and the third term is a + 2d.<\/h3>\n<h3>According to the problem, we have:<\/h3>\n<h3>a + d = 14 (1) a + 2d = 18 (2)<\/h3>\n<h3>Subtracting equation (1) from equation (2), we get:<\/h3>\n<h3>d = 4<\/h3>\n<h3>Substituting this value of d into equation (1), we get:<\/h3>\n<h3>a + 4 = 14<\/h3>\n<h3>a = 10<\/h3>\n<h3>Therefore, the AP is: 10, 14, 18, 22, &#8230;<\/h3>\n<h3>The sum of the first n terms of an AP is given by the formula:<\/h3>\n<h3>S_n = n\/2 [2a + (n-1)d]<\/h3>\n<h3>Substituting a = 10, d = 4, and n = 51, we get:<\/h3>\n<h3>S_51 = 51\/2 [2(10) + (51-1)4] = 51\/2 [20 + 200] = 51\/2 x 220 = 5625<\/h3>\n<h3>Therefore, the sum of the first 51 terms of the AP is 5625.<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Question :Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18, respectively. The correct answer :Let the first term of the AP be a and the common difference be d. Then, the second term is a + d, and the third term is a + 2d. [&hellip;]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-134823","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134823","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=134823"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134823\/revisions"}],"predecessor-version":[{"id":134824,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134823\/revisions\/134824"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=134823"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=134823"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=134823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}