{"id":304083,"date":"2022-09-10T22:50:16","date_gmt":"2022-09-10T17:20:16","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/given-sum-of-first-n-terms-of-an-ap-is-2n-3n2-another-ap-is-formed-with-the-same-first-term-and-double-of-the-common-difference-the-sum-of-n-terms-of-the-new-ap-is\/"},"modified":"2022-09-10T22:50:16","modified_gmt":"2022-09-10T17:20:16","slug":"given-sum-of-first-n-terms-of-an-ap-is-2n-3n2-another-ap-is-formed-with-the-same-first-term-and-double-of-the-common-difference-the-sum-of-n-terms-of-the-new-ap-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/given-sum-of-first-n-terms-of-an-ap-is-2n--3n2-another-ap\/","title":{"rendered":"Given sum of first n terms of an AP is 2n + 3n2. Another AP is formed with the same first term and double of the common difference, the sum of n terms of the new AP is:\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Given sum of first n terms of an AP is 2n + 3n2. Another AP is formed with the same first term and double of the common difference, the sum of n terms of the new AP is:\u00a0","custom_permalink":"question\/mathematics\/given-sum-of-first-n-terms-of-an-ap-is-2n--3n2-another-ap\/"},"categories":[],"acf":{"question":"

Given sum of first n terms of an AP is 2n + 3n2<\/sup>. Another AP is formed with the same first term and double of the common difference, the sum of n terms of the new AP is: <\/span><\/p>","options":[{"option":"

n<\/mi>+<\/mo>4<\/mn>n<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":false},{"option":"

6<\/mn>n<\/mi>2<\/mn><\/msup>\u2212<\/mo>n<\/mi><\/math><\/p>","correct":true},{"option":"

n<\/mi>2<\/mn><\/msup>+<\/mo>4<\/mn>n<\/mi><\/math><\/p>","correct":false},{"option":"

3<\/mn>n<\/mi>+<\/mo>2<\/mn>n<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":false}],"solution":"

G<\/mi>i<\/mi>v<\/mi>e<\/mi>n<\/mi> <\/mo>s<\/mi>u<\/mi>m<\/mi> <\/mo>o<\/mi>f<\/mi> <\/mo>n<\/mi> <\/mo>t<\/mi>e<\/mi>r<\/mi>m<\/mi>s<\/mi> <\/mo>o<\/mi>f<\/mi> <\/mo>A<\/mi>P<\/mi>\u2009<\/mo>i<\/mi>s<\/mi> <\/mo>S<\/mi>n<\/mi><\/msub>=<\/mo>2<\/mn>n<\/mi>+<\/mo>3<\/mn>n<\/mi>2<\/mn><\/msup> <\/mspace>F<\/mi>o<\/mi>r<\/mi> <\/mo>t<\/mi>h<\/mi>e<\/mi> <\/mo>f<\/mi>i<\/mi>r<\/mi>s<\/mi>t<\/mi> <\/mo>t<\/mi>e<\/mi>r<\/mi>m<\/mi> <\/mo>s<\/mi>u<\/mi>b<\/mi>s<\/mi>t<\/mi>i<\/mi>t<\/mi>u<\/mi>t<\/mi>e<\/mi> <\/mo>n<\/mi>=<\/mo>1<\/mn> <\/mspace>H<\/mi>e<\/mi>n<\/mi>c<\/mi>e<\/mi>,<\/mo> <\/mo>a<\/mi>1<\/mn><\/msub> <\/mo>=<\/mo> <\/mo>5<\/mn> <\/mspace>T<\/mi>h<\/mi>e<\/mi> <\/mo>s<\/mi>e<\/mi>c<\/mi>o<\/mi>n<\/mi>d<\/mi> <\/mo>t<\/mi>e<\/mi>r<\/mi>m<\/mi> <\/mo>i<\/mi>s<\/mi> <\/mo>a<\/mi>2<\/mn><\/msub>=<\/mo>S<\/mi>2<\/mn><\/msub>-<\/mo>S<\/mi>1<\/mn><\/msub>=<\/mo>16<\/mn>-<\/mo>5<\/mn>=<\/mo>11<\/mn> <\/mspace>T<\/mi>h<\/mi>e<\/mi> <\/mo>c<\/mi>o<\/mi>m<\/mi>m<\/mi>o<\/mi>n<\/mi> <\/mo>d<\/mi>i<\/mi>f<\/mi>f<\/mi>e<\/mi>r<\/mi>e<\/mi>n<\/mi>c<\/mi>e<\/mi> <\/mo>i<\/mi>s<\/mi> <\/mo>a<\/mi>2<\/mn><\/msub>-<\/mo>a<\/mi>1<\/mn><\/msub>=<\/mo>11<\/mn>-<\/mo>5<\/mn>=<\/mo>6<\/mn> <\/mspace>H<\/mi>e<\/mi>n<\/mi>c<\/mi>e<\/mi>,<\/mo> <\/mo>t<\/mi>h<\/mi>e<\/mi> <\/mo>f<\/mi>i<\/mi>r<\/mi>s<\/mi>t<\/mi> <\/mo>t<\/mi>e<\/mi>r<\/mi>m<\/mi> <\/mo>a<\/mi>n<\/mi>d<\/mi> <\/mo>c<\/mi>o<\/mi>m<\/mi>m<\/mi>o<\/mi>n<\/mi> <\/mo>d<\/mi>i<\/mi>f<\/mi>f<\/mi>e<\/mi>r<\/mi>e<\/mi>n<\/mi>c<\/mi>e<\/mi> <\/mo>o<\/mi>f<\/mi> <\/mo>t<\/mi>h<\/mi>e<\/mi> <\/mo>o<\/mi>r<\/mi>i<\/mi>g<\/mi>i<\/mi>n<\/mi>a<\/mi>l<\/mi> <\/mo>s<\/mi>e<\/mi>q<\/mi>u<\/mi>e<\/mi>n<\/mi>c<\/mi>e<\/mi> <\/mo>a<\/mi>r<\/mi>e<\/mi> <\/mo>a<\/mi>1<\/mn><\/msub> <\/mo>=<\/mo>5<\/mn>,<\/mo> <\/mo>d<\/mi>=<\/mo>6<\/mn><\/math><\/p>

F<\/mi>o<\/mi>r<\/mi> <\/mo>t<\/mi>h<\/mi>e<\/mi> <\/mo>n<\/mi>e<\/mi>w<\/mi> <\/mo>s<\/mi>e<\/mi>q<\/mi>u<\/mi>n<\/mi>c<\/mi>e<\/mi>,<\/mo> <\/mo>f<\/mi>i<\/mi>r<\/mi>s<\/mi>t<\/mi> <\/mo>t<\/mi>e<\/mi>r<\/mi>m<\/mi> <\/mo>i<\/mi>s<\/mi> <\/mo>s<\/mi>a<\/mi>m<\/mi>e<\/mi> <\/mo>a<\/mi><\/mtd>=<\/mo><\/mtd>5<\/mn> <\/mo>o<\/mi>n<\/mi>l<\/mi>y<\/mi><\/mtd><\/mtr> <\/mtd> <\/mtd>C<\/mi>o<\/mi>m<\/mi>m<\/mi>o<\/mi>n<\/mi> <\/mo>d<\/mi>i<\/mi>f<\/mi>f<\/mi>e<\/mi>r<\/mi>e<\/mi>n<\/mi>c<\/mi>e<\/mi> <\/mo>i<\/mi>s<\/mi> <\/mo>t<\/mi>w<\/mi>o<\/mi> <\/mo>t<\/mi>i<\/mi>m<\/mi>e<\/mi>s<\/mi> <\/mo>o<\/mi>f<\/mi> <\/mo>6<\/mn><\/mtd><\/mtr>d<\/mi><\/mtd>=<\/mo><\/mtd>12<\/mn><\/mtd><\/mtr>S<\/mi>u<\/mi>m<\/mi> <\/mo>o<\/mi>f<\/mi> <\/mo>f<\/mi>i<\/mi>r<\/mi>s<\/mi>t<\/mi> <\/mo>n<\/mi> <\/mo>t<\/mi>e<\/mi>r<\/mi>m<\/mi>s<\/mi> <\/mo>o<\/mi>f<\/mi> <\/mo>n<\/mi>e<\/mi>w<\/mi> <\/mo>A<\/mi>P<\/mi> <\/mo>i<\/mi>s<\/mi> <\/mo>S<\/mi>n<\/mi><\/msub><\/mtd>=<\/mo><\/mtd>n<\/mi>2<\/mn><\/mfrac>2<\/mn>a<\/mi>+<\/mo>n<\/mi>-<\/mo>1<\/mn><\/mrow><\/mfenced>d<\/mi><\/mrow><\/mfenced><\/mtd><\/mtr>S<\/mi>n<\/mi><\/msub><\/mtd>=<\/mo><\/mtd>n<\/mi>2<\/mn><\/mfrac>10<\/mn>+<\/mo>(<\/mo>n<\/mi>-<\/mo>1<\/mn>)<\/mo>12<\/mn><\/mrow><\/mfenced><\/mtd><\/mtr> <\/mtd>=<\/mo><\/mtd>6<\/mn>n<\/mi>n<\/mi><\/mfenced>-<\/mo>n<\/mi><\/mtd><\/mtr> <\/mtd>=<\/mo><\/mtd>6<\/mn>n<\/mi>2<\/mn><\/msup>-<\/mo>n<\/mi><\/mtd><\/mtr><\/mtable><\/math><\/p>

 <\/p>","subject":""},"yoast_head":"\nGiven sum of first n terms of an AP is 2n + 3n2. Another AP is formed with the same first term and double of the common difference, the sum of n terms of the new AP is:\u00a0 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Given sum of first n terms of an AP is 2n + 3n2. Another AP is formed with the same first term and double of the common difference, the sum of n terms of the new AP is:\u00a0\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/given-sum-of-first-n-terms-of-an-ap-is-2n--3n2-another-ap\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Given sum of first n terms of an AP is 2n + 3n2. 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