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

According to the question:

              49 = 7*(a + 3d)

  7= a + 3d

We can observe that it is 4^th term,

Similarly,

S_{17 =17/2 [2a+(16)d]}

289 = 17(a + 8d)

17 = a + 8d

We can observe that it is 9^th term,

This is the 9th term

Subtracting 4^th term from 9^th term, we get;

a + 8d – a – 3d = 17 – 7

Or, 5d = 10

Or, d = 2

Using the value of d in equation for fourth term, we can find a as follows:

a + 3d =7

Or, a + 6 = 7

Or, a = 1

Using the values of a and d; we can find the sum of first n terms as follows:

    N²