The sum of first n terms of an AP is (5n – n 2 ). The nth term of the 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 = 5n - n²

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

∴ a_n = (5n - n²) - [5(n - 1) - (n - 1)²]

= (5n - n²) - [5n - 5 - (n² + 1 - 2n)]

= 5n - n² - 5n + 5 + n² + 1 - 2n

= 6 - 2n

The sum of first n terms of an AP is (5n – n2). The nth term of the AP is