The sum of first n terms of an AP is (4n 2 + 2n). The nth term of this AP is

Question

Philoid · Accepted Answer

Let S_n denotes the sum of first n terms of an AP.

Sum of first n terms = S_n = 4n² + 2n

Then n^th term is given by: a_n = S_n - S_{n - 1}

∴ a_n = (4n² + 2n) - [4(n - 1)² + 2(n - 1)]

= (4n² + 2n) - [4(n² + 1 - 2n) + 2n - 2]

= 4n² + 2n - 4n² - 4 + 8n - 2n + 2

= 8n - 2