If the sum of 7 terms of an A.P. is 49 and that of 17 term is 289, find the sum of n terms.
S7= 49
[2a + 6d] = 49
a + 3d = 7 (i)
S17= 289
[2a + 16d] = 289
a + 8d = 17 (ii)
Subtract (i) from (ii), we get
5d = 10
d = 2
Put d = 2 in (i), we get
a = 7 – 6 = 1
Sn= 
[2(1) + (n – 1)2]
= n [1 + n – 1]
= n2
29