Question

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.

Answer 1

A.P such that S₇ = 49; S₁₇ = 289

We know that,

Substituting d = 2 in equation (1), we get, 

a + 3 × 2 = 7 

⇒ a = 7 – 6 = 1

∴ a = 1; d = 2

∴ Sum of first n terms S_n = n². 

Shortcut: S₇ = 49 = 7² 

S₁₇ = 289 = 17² 

∴ S_n = n²