Question

Sum of first 7 terms of an AP is 49 and that of 17 terms is 289.Find sum of first n terms.

Answer 1

We are given, S7 = 49
            so, 7/2 [2a + 6d] = 49
            so, a+ 3d = 7 ................(1)
  
         S17 = 289
        17/2[2a + 16d] = 289
        so,  a + 8d = 17 ..........(2)

On, Solving Eqn (1) & (2)

We get, a = 1 and d = 2 

So, Sn = n/2 [2a + (n-1)d]
            = n/2 [2*1 + (n-1)2]
            = n/2 [2 + 2n -2] 
            = n/2 [2n] = n*n = n²

Answer 2

now put this value in the formula of sn you will get answer