Question

In an AP, if the sum of first seven terms is 49 and that of seventeen terms is 289, find the sum of first n terms.

Answer 1

⇒S7 = 7 * (a1 + a7) / 2 = 49 
⇒7(a1 + a1 + 6d) / 2 = 49 
⇒2a1 + 6d = 14 
⇒S17 = 17 * (a1 + a17) / 2 = 289 
⇒17(a1 + a1 + 16d) / 2 = 289 
⇒a1 + 8d = 17 
==> We have : 
⇒2a1 + 6d = 14 
⇒a1 + 8d = 17 
⇒a = 1, d = 2 
⇒an = 1 + (n - 1)*2 
⇒an = 2n - 1

Answer 2

Ur answer is attached above with 3 pics.

Sn=n^2

a=1

d=2