{"id":93121,"date":"2025-06-01T11:42:17","date_gmt":"2025-06-01T11:42:17","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93121"},"modified":"2025-06-01T11:42:17","modified_gmt":"2025-06-01T11:42:17","slug":"the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/","title":{"rendered":"The sum of the numbers 3, 6, 9, 12, &#8230; up to the 20 th  term is :"},"content":{"rendered":"<p>The sum of the numbers 3, 6, 9, 12, &#8230; up to the 20<sup>th<\/sup> term is :<\/p>\n<p>[amp_mcq option1=&#8221;600&#8243; option2=&#8221;1260&#8243; option3=&#8221;630&#8243; option4=&#8221;960&#8243; correct=&#8221;option3&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC CISF-AC-EXE &#8211; 2022<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-cisf-ac-exe-2022.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-cisf-ac-exe-2022\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nThe given sequence is 3, 6, 9, 12, &#8230; which is an arithmetic progression (AP).<br \/>\nThe first term (a) is 3.<br \/>\nThe common difference (d) is 6 &#8211; 3 = 3 (or 9 &#8211; 6 = 3, etc.).<br \/>\nWe need to find the sum of the first 20 terms (n = 20).<br \/>\nThe formula for the sum of the first n terms of an AP is S<sub>n<\/sub> = n\/2 * [2a + (n-1)d].<br \/>\nSubstituting the values:<br \/>\nS<sub>20<\/sub> = 20\/2 * [2 * 3 + (20 &#8211; 1) * 3]<br \/>\nS<sub>20<\/sub> = 10 * [6 + 19 * 3]<br \/>\nS<sub>20<\/sub> = 10 * [6 + 57]<br \/>\nS<sub>20<\/sub> = 10 * 63<br \/>\nS<sub>20<\/sub> = 630<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\n&#8211; Recognize the sequence as an Arithmetic Progression (AP).<br \/>\n&#8211; Identify the first term (a) and the common difference (d).<br \/>\n&#8211; Use the formula for the sum of the first n terms of an AP: S<sub>n<\/sub> = n\/2 * [2a + (n-1)d].<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nAlternatively, the sequence is 3 * 1, 3 * 2, 3 * 3, &#8230;, 3 * 20.<br \/>\nThe sum is 3 * (1 + 2 + 3 + &#8230; + 20).<br \/>\nThe sum of the first n natural numbers is n(n+1)\/2.<br \/>\nSo, the sum of 1 to 20 is 20(20+1)\/2 = 20 * 21 \/ 2 = 10 * 21 = 210.<br \/>\nThe sum of the sequence is 3 * 210 = 630.<br \/>\nThis confirms the result obtained using the AP sum formula.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>The sum of the numbers 3, 6, 9, 12, &#8230; up to the 20th term is : [amp_mcq option1=&#8221;600&#8243; option2=&#8221;1260&#8243; option3=&#8221;630&#8243; option4=&#8221;960&#8243; correct=&#8221;option3&#8243;] This question was previously asked in UPSC CISF-AC-EXE &#8211; 2022 Download PDFAttempt Online The given sequence is 3, 6, 9, 12, &#8230; which is an arithmetic progression (AP). The first term (a) &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"The sum of the numbers 3, 6, 9, 12, &#8230; up to the 20 th  term is :\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/#more-93121\">Detailed Solution<span class=\"screen-reader-text\">The sum of the numbers 3, 6, 9, 12, &#8230; up to the 20 th  term is :<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1089],"tags":[1108,1102],"class_list":["post-93121","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The sum of the numbers 3, 6, 9, 12, ... up to the 20 th term is :<\/title>\n<meta name=\"description\" content=\"The given sequence is 3, 6, 9, 12, ... which is an arithmetic progression (AP). The first term (a) is 3. The common difference (d) is 6 - 3 = 3 (or 9 - 6 = 3, etc.). We need to find the sum of the first 20 terms (n = 20). The formula for the sum of the first n terms of an AP is Sn = n\/2 * [2a + (n-1)d]. Substituting the values: S20 = 20\/2 * [2 * 3 + (20 - 1) * 3] S20 = 10 * [6 + 19 * 3] S20 = 10 * [6 + 57] S20 = 10 * 63 S20 = 630 - Recognize the sequence as an Arithmetic Progression (AP). - Identify the first term (a) and the common difference (d). - Use the formula for the sum of the first n terms of an AP: Sn = n\/2 * [2a + (n-1)d].\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The sum of the numbers 3, 6, 9, 12, ... up to the 20 th term is :\" \/>\n<meta property=\"og:description\" content=\"The given sequence is 3, 6, 9, 12, ... which is an arithmetic progression (AP). The first term (a) is 3. The common difference (d) is 6 - 3 = 3 (or 9 - 6 = 3, etc.). We need to find the sum of the first 20 terms (n = 20). The formula for the sum of the first n terms of an AP is Sn = n\/2 * [2a + (n-1)d]. Substituting the values: S20 = 20\/2 * [2 * 3 + (20 - 1) * 3] S20 = 10 * [6 + 19 * 3] S20 = 10 * [6 + 57] S20 = 10 * 63 S20 = 630 - Recognize the sequence as an Arithmetic Progression (AP). - Identify the first term (a) and the common difference (d). - Use the formula for the sum of the first n terms of an AP: Sn = n\/2 * [2a + (n-1)d].\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:42:17+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The sum of the numbers 3, 6, 9, 12, ... up to the 20 th term is :","description":"The given sequence is 3, 6, 9, 12, ... which is an arithmetic progression (AP). The first term (a) is 3. The common difference (d) is 6 - 3 = 3 (or 9 - 6 = 3, etc.). We need to find the sum of the first 20 terms (n = 20). The formula for the sum of the first n terms of an AP is Sn = n\/2 * [2a + (n-1)d]. Substituting the values: S20 = 20\/2 * [2 * 3 + (20 - 1) * 3] S20 = 10 * [6 + 19 * 3] S20 = 10 * [6 + 57] S20 = 10 * 63 S20 = 630 - Recognize the sequence as an Arithmetic Progression (AP). - Identify the first term (a) and the common difference (d). - Use the formula for the sum of the first n terms of an AP: Sn = n\/2 * [2a + (n-1)d].","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/","og_locale":"en_US","og_type":"article","og_title":"The sum of the numbers 3, 6, 9, 12, ... up to the 20 th term is :","og_description":"The given sequence is 3, 6, 9, 12, ... which is an arithmetic progression (AP). The first term (a) is 3. The common difference (d) is 6 - 3 = 3 (or 9 - 6 = 3, etc.). We need to find the sum of the first 20 terms (n = 20). The formula for the sum of the first n terms of an AP is Sn = n\/2 * [2a + (n-1)d]. Substituting the values: S20 = 20\/2 * [2 * 3 + (20 - 1) * 3] S20 = 10 * [6 + 19 * 3] S20 = 10 * [6 + 57] S20 = 10 * 63 S20 = 630 - Recognize the sequence as an Arithmetic Progression (AP). - Identify the first term (a) and the common difference (d). - Use the formula for the sum of the first n terms of an AP: Sn = n\/2 * [2a + (n-1)d].","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:42:17+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/","name":"The sum of the numbers 3, 6, 9, 12, ... up to the 20 th term is :","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:42:17+00:00","dateModified":"2025-06-01T11:42:17+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The given sequence is 3, 6, 9, 12, ... which is an arithmetic progression (AP). The first term (a) is 3. The common difference (d) is 6 - 3 = 3 (or 9 - 6 = 3, etc.). We need to find the sum of the first 20 terms (n = 20). The formula for the sum of the first n terms of an AP is Sn = n\/2 * [2a + (n-1)d]. Substituting the values: S20 = 20\/2 * [2 * 3 + (20 - 1) * 3] S20 = 10 * [6 + 19 * 3] S20 = 10 * [6 + 57] S20 = 10 * 63 S20 = 630 - Recognize the sequence as an Arithmetic Progression (AP). - Identify the first term (a) and the common difference (d). - Use the formula for the sum of the first n terms of an AP: Sn = n\/2 * [2a + (n-1)d].","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-the-numbers-3-6-9-12-up-to-the-20-th-term-is\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CISF-AC-EXE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cisf-ac-exe\/"},{"@type":"ListItem","position":3,"name":"The sum of the numbers 3, 6, 9, 12, &#8230; up to the 20 th term is :"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93121","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=93121"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93121\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=93121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=93121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=93121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}