{"id":134825,"date":"2023-03-21T16:41:24","date_gmt":"2023-03-21T11:11:24","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=134825"},"modified":"2023-03-21T16:41:24","modified_gmt":"2023-03-21T11:11:24","slug":"the-first-term-of-an-a-p-is-5-the-last-term-is-45-and-the-sum-is-400-find-the-number-of-terms-and-the-common-difference","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/the-first-term-of-an-a-p-is-5-the-last-term-is-45-and-the-sum-is-400-find-the-number-of-terms-and-the-common-difference","title":{"rendered":"The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference."},"content":{"rendered":"<h2>Question :The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.<\/h2>\n<h3>The correct answer :Let there be n terms in the arithmetic progression (AP), and let the common difference be d. Then, we have:<\/h3>\n<h3>The nth term = a + (n-1)d where a is the first term.<\/h3>\n<h3>According to the problem, we have:<\/h3>\n<h3>a = 5 (first term) a + (n-1)d = 45 (last term) n\/2 [2a + (n-1)d] = 400 (sum of n terms)<\/h3>\n<h3>Substituting a = 5 and a + (n-1)d = 45, we get:<\/h3>\n<h3>5 + (n-1)d = 45 n = 41\/d + 1<\/h3>\n<h3>Substituting these values into the third equation, we get:<\/h3>\n<h3>n\/2 [10 + (n-1)d] = 400<\/h3>\n<h3>Substituting n = 41\/d + 1, we get:<\/h3>\n<h3>(41\/d + 1)\/2 [10 + (41\/d) d &#8211; d] = 400<\/h3>\n<h3>Simplifying, we get:<\/h3>\n<h3>(41\/d + 1)\/2 [10 + 40] = 400<\/h3>\n<h3>Multiplying both sides by 2, we get:<\/h3>\n<h3>(41\/d + 1) x 25 = 800<\/h3>\n<h3>Expanding, we get:<\/h3>\n<h3>41\/d + 1 = 32<\/h3>\n<h3>Subtracting 1 from both sides, we get:<\/h3>\n<h3>41\/d = 31<\/h3>\n<h3>Multiplying both sides by d, we get:<\/h3>\n<h3>d = 41\/31<\/h3>\n<h3>Substituting d = 41\/31 into the equation n = 41\/d + 1, we get:<\/h3>\n<h3>n = 41\/(41\/31) + 1 = 32<\/h3>\n<h3>Therefore, the common difference is d = 41\/31 and the number of terms is n = 32.<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Question :The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference. The correct answer :Let there be n terms in the arithmetic progression (AP), and let the common difference be d. Then, we have: The nth term = [&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-134825","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\/134825","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=134825"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134825\/revisions"}],"predecessor-version":[{"id":134826,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134825\/revisions\/134826"}],"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=134825"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=134825"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=134825"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}