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| 1. |
The sum of first 7 terms is 49 and that of first 17 terms is 289 . Find the sum of first n terms . |
| Answer» Sn= {tex}\\frac n2{/tex}[2a + (n - 1)d]S7\xa0=\xa0{tex}\\frac 72{/tex}(2a + 6d) = 49or, {tex}a + 3d = 7{/tex}...........(i)S17\xa0=\xa0{tex}\\frac{17}{2}{/tex}(2a + 16d) = 289or, {tex}a + 8d = 17{/tex}..........(ii)On subtracting (i) from (ii), we getor, 5d = 10 or, d = 2Put d = 2 in (i)a + 3d = 7a + 2(3) = 7a + 6 = 7and a = 1{tex}S _ { n } = \\frac { n } { 2 } [ 2 \\times 1 + ( n - 1 ) 2 ]{/tex}{tex}= \\frac { n } { 2 } [ 2 + 2 n - 2 ] {/tex}{tex}= \\frac { n } { 2 } [ 2 n ] {/tex}{tex}= n ^ { 2 }{/tex}Hence, sum of n terms = n2 | |