9. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Given that, S7 = 49 S17 = 289 We know, Sum of n terms; Sn = n/2 [2a + (n – 1)d] Therefore, S7= 7/2 [2a +(n -1)d] S7 = 7/2 [2a + (7 -1)d] 49 = 7/2 [2a +6d] 7 = (a+3d) a + 3d = 7 …………………………………. (i) In the same way, S17 = 17/2 [2a+(17-1)d] 289 = 17/2 (2a +16d) 17 = (a+8d) a +8d = 17 ………………………………. (ii) Subtracting equation (i) from equation (ii), 5d = 10 d = 2 From equation (i), we can write it as; a+3(2) = 7 a+ 6 = 7 a = 1 Hence, Sn = n/2[2a+(n-1)d] = n/2[2(1)+(n – 1)×2] = n/2(2+2n-2) = n/2(2n) = n2