(Q28).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 :

A.P such that S7 = ; S17 =

We know that,

Sn =
n
2
 [2a+(n-1)d]
=
2
 [a+(-1)d]
⇒
=
1
2
 [a+d]

⇒ = a + d .........(1)

Also, S17 = =
2
 [a + ( - 1)d]
⇒
=
1
2
 [a+d]

⇒ = a + d .........(2)

equation (2); a + d =
equation (1); a + d =

d =

⇒ d =
=

Substituting d = in equation (1), we get,

a + × =

⇒ a = – =

∴ a = ; d =

Now, Sn =
n
2
 [2a+(n-1)d]
Sn =
n
2
 [2 × +(n-1)]
=
n
2
 [ + n-] =
n.n
2

∴ Sum of first n terms Sn = n2.

Shortcut: S7 = = 2

S17 = = 2

∴ Sn = n2