{"id":302438,"date":"2022-09-10T22:19:21","date_gmt":"2022-09-10T16:49:21","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/let-s1s2s3-and-t1t2t3-are-two-arithmetic-sequences-such-that-s1t1%e2%89%a00s22t2-an\/"},"modified":"2022-09-10T22:19:21","modified_gmt":"2022-09-10T16:49:21","slug":"let-s1s2s3-and-t1t2t3-are-two-arithmetic-sequences-such-that-s1t1%e2%89%a00s22t2-an","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/lets1s2s3andt1t2t3are-two-arithmetic-seque\/","title":{"rendered":"\u00a0Let\u00a0S1,S2,S3\u2026\u2026\u2026\u2026.\u00a0and\u00a0t1,t2,t3\u2026\u2026\u2026\u2026.\u00a0are two arithmetic sequences such that\u00a0S1=t1\u22600;S2=2t2\u00a0and\u00a0\u2211i=110\u200aSi=\u2211i=115\u200ati\u00a0then, the value of\u00a0S2\u2212S1t2\u2212t1\u00a0is:\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\u00a0Let\u00a0S1,S2,S3\u2026\u2026\u2026\u2026.\u00a0and\u00a0t1,t2,t3\u2026\u2026\u2026\u2026.\u00a0are two arithmetic sequences such that\u00a0S1=t1\u22600;S2=2t2\u00a0and\u00a0\u2211i=110\u200aSi=\u2211i=115\u200ati\u00a0then, the value of\u00a0S2\u2212S1t2\u2212t1\u00a0is:\u00a0","custom_permalink":"question\/mathematics\/lets1s2s3andt1t2t3are-two-arithmetic-seque\/"},"categories":[],"acf":{"question":"

 Let <\/mtext>S<\/mi>1<\/mn><\/msub>,<\/mo>S<\/mi>2<\/mn><\/msub>,<\/mo>S<\/mi>3<\/mn><\/msub>\u2026<\/mo>\u2026<\/mo>\u2026<\/mo>\u2026<\/mo>.<\/mo> and <\/mtext>t<\/mi>1<\/mn><\/msub>,<\/mo>t<\/mi>2<\/mn><\/msub>,<\/mo>t<\/mi>3<\/mn><\/msub>\u2026<\/mo>\u2026<\/mo>\u2026<\/mo>\u2026<\/mo>.<\/mo> are two arithmetic sequences such that <\/mtext><\/math>S<\/mi>1<\/mn><\/msub>=<\/mo>t<\/mi>1<\/mn><\/msub>\u2260<\/mo>0<\/mn>;<\/mo>S<\/mi>2<\/mn><\/msub>=<\/mo>2<\/mn>t<\/mi>2<\/mn><\/msub> and <\/mtext>\u2211<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>10<\/mn><\/munderover>\u200a<\/mo>S<\/mi>i<\/mi><\/msub>=<\/mo>\u2211<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>15<\/mn><\/munderover>\u200a<\/mo>t<\/mi>i<\/mi><\/msub> then, the value of <\/mtext>S<\/mi>2<\/mn><\/msub>\u2212<\/mo>S<\/mi>1<\/mn><\/msub><\/mrow>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>t<\/mi>1<\/mn><\/msub><\/mrow><\/mfrac> is: <\/mtext><\/math><\/p>","options":[{"option":"

8<\/mn>3<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"

3<\/mn>2<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"

19<\/mn>8<\/mn><\/mfrac><\/math><\/p>","correct":true},{"option":"

2<\/p>","correct":false}],"solution":"

 Let <\/mtext>S<\/mi>1<\/mn>,<\/mo><\/mrow><\/msub>S<\/mi>2<\/mn><\/msub>,<\/mo>S<\/mi>3<\/mn><\/msub>\u2026<\/mo>\u2026<\/mo>\u2026<\/mo>\u2026<\/mo>.<\/mo> are in A.P. with common difference <\/mtext>d<\/mi> and <\/mtext>t<\/mi>1<\/mn><\/msub>,<\/mo>t<\/mi>2<\/mn><\/msub>,<\/mo>t<\/mi>3<\/mn><\/msub> are <\/mtext><\/math><\/p>

 in A.P with common difference <\/mtext>d<\/mi>2<\/mn><\/msub>. <\/mtext><\/math><\/p>

\u2211<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>10<\/mn><\/munderover>\u200a<\/mo>S<\/mi>i<\/mi><\/msub>=<\/mo>10<\/mn>2<\/mn><\/mfrac>2<\/mn>S<\/mi>1<\/mn><\/msub>+<\/mo>(<\/mo>10<\/mn>\u2212<\/mo>1<\/mn>)<\/mo>d<\/mi>1<\/mn><\/msub><\/mrow><\/mfenced><\/mtd><\/mtr>\u2211<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>15<\/mn><\/munderover>\u200a<\/mo>t<\/mi>i<\/mi><\/msub>=<\/mo>15<\/mn>2<\/mn><\/mfrac>2<\/mn>t<\/mi>1<\/mn><\/msub>+<\/mo>(<\/mo>15<\/mn>\u2212<\/mo>1<\/mn>)<\/mo>d<\/mi>2<\/mn><\/msub><\/mrow><\/mfenced><\/mtd><\/mtr>10<\/mn>2<\/mn>S<\/mi>1<\/mn><\/msub>+<\/mo>9<\/mn>d<\/mi>1<\/mn><\/msub><\/mrow><\/mfenced>=<\/mo>15<\/mn>2<\/mn>t<\/mi>1<\/mn><\/msub>+<\/mo>14<\/mn>d<\/mi>2<\/mn><\/msub><\/mrow><\/mfenced><\/mtd><\/mtr>2<\/mn>2<\/mn>S<\/mi>1<\/mn><\/msub>+<\/mo>9<\/mn>d<\/mi>1<\/mn><\/msub><\/mrow><\/mfenced>=<\/mo>3<\/mn>2<\/mn>t<\/mi>1<\/mn><\/msub>+<\/mo>14<\/mn>d<\/mi>2<\/mn><\/msub><\/mrow><\/mfenced><\/mtd><\/mtr>2<\/mn>S<\/mi>1<\/mn><\/msub>+<\/mo>9<\/mn>d<\/mi>1<\/mn><\/msub>=<\/mo>3<\/mn>t<\/mi>1<\/mn><\/msub>+<\/mo>7<\/mn>d<\/mi>2<\/mn><\/msub><\/mrow><\/mfenced><\/mtd><\/mtr>2<\/mn>S<\/mi>1<\/mn><\/msub>+<\/mo>9<\/mn>d<\/mi>1<\/mn><\/msub>=<\/mo>3<\/mn>t<\/mi>1<\/mn><\/msub>+<\/mo>21<\/mn>d<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>As<\/mi>,<\/mo> <\/mspace>S<\/mi>1<\/mn><\/msub>=<\/mo>t<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>2<\/mn>t<\/mi>1<\/mn><\/msub>+<\/mo>9<\/mn>d<\/mi>1<\/mn><\/msub>=<\/mo>3<\/mn>t<\/mi>1<\/mn><\/msub>+<\/mo>21<\/mn>d<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>9<\/mn>d<\/mi>1<\/mn><\/msub>=<\/mo>t<\/mi>1<\/mn><\/msub>+<\/mo>21<\/mn>d<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>d<\/mi>1<\/mn><\/msub>=<\/mo>S<\/mi>2<\/mn><\/msub>\u2212<\/mo>S<\/mi>1<\/mn><\/msub>=<\/mo>2<\/mn>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>t<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>d<\/mi>2<\/mn><\/msub>=<\/mo>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>t<\/mi>1<\/mn><\/msub><\/mtd><\/mtr><\/mtable><\/math><\/p>

9<\/mn>2<\/mn>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>t<\/mi>1<\/mn><\/msub><\/mrow><\/mfenced>=<\/mo>t<\/mi>1<\/mn><\/msub>+<\/mo>21<\/mn>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>21<\/mn>t<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>18<\/mn>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>9<\/mn>t<\/mi>1<\/mn><\/msub>=<\/mo>21<\/mn>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>20<\/mn>t<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>11<\/mn>t<\/mi>1<\/mn><\/msub>=<\/mo>3<\/mn>t<\/mi>2<\/mn><\/msub><\/mtd><\/mtr> Thus, <\/mtext>S<\/mi>2<\/mn><\/msub>\u2212<\/mo>S<\/mi>1<\/mn><\/msub><\/mrow>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>t<\/mi>1<\/mn><\/msub><\/mrow><\/mfrac>=<\/mo>2<\/mn>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>t<\/mi>1<\/mn><\/msub><\/mrow>t<\/mi>2<\/mn><\/msub>\u2212<\/mo>t<\/mi>1<\/mn><\/msub><\/mrow><\/mfrac>=<\/mo>2<\/mn>\u22c5<\/mo>11<\/mn>3<\/mn><\/mfrac>\u2212<\/mo>1<\/mn><\/mrow>11<\/mn>3<\/mn><\/mfrac>\u2212<\/mo>1<\/mn><\/mrow><\/mfrac>=<\/mo>22<\/mn>\u2212<\/mo>3<\/mn><\/mrow>8<\/mn><\/mfrac>=<\/mo>19<\/mn>8<\/mn><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"\n\u00a0Let\u00a0S1,S2,S3\u2026\u2026\u2026\u2026.\u00a0and\u00a0t1,t2,t3\u2026\u2026\u2026\u2026.\u00a0are two arithmetic sequences such that\u00a0S1=t1\u22600;S2=2t2\u00a0and\u00a0\u2211i=110\u200aSi=\u2211i=115\u200ati\u00a0then, the value of\u00a0S2\u2212S1t2\u2212t1\u00a0is:\u00a0 - 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Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-09-10T16:49:21+00:00","dateModified":"2022-09-10T16:49:21+00:00","description":"\u00a0Let\u00a0S1,S2,S3\u2026\u2026\u2026\u2026.\u00a0and\u00a0t1,t2,t3\u2026\u2026\u2026\u2026.\u00a0are two arithmetic sequences such that\u00a0S1=t1\u22600;S2=2t2\u00a0and\u00a0\u2211i=110\u200aSi=\u2211i=115\u200ati\u00a0then, the value of\u00a0S2\u2212S1t2\u2212t1\u00a0is:\u00a0","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/lets1s2s3andt1t2t3are-two-arithmetic-seque\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/mathematics\/lets1s2s3andt1t2t3are-two-arithmetic-seque\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/lets1s2s3andt1t2t3are-two-arithmetic-seque\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"\u00a0Let\u00a0S1,S2,S3\u2026\u2026\u2026\u2026.\u00a0and\u00a0t1,t2,t3\u2026\u2026\u2026\u2026.\u00a0are two arithmetic sequences such that\u00a0S1=t1\u22600;S2=2t2\u00a0and\u00a0\u2211i=110\u200aSi=\u2211i=115\u200ati\u00a0then, the value of\u00a0S2\u2212S1t2\u2212t1\u00a0is:\u00a0"}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/302438"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=302438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=302438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}