Question

The sum of the first n terms of an AP is given by S_n = (2n² + 5n). Find the nth term of the AP.

Answer 1

Given: S_n = (2n² + 5n) ...(i)
Replacing n by (n - 1) in (i), we get:
S_n-1 = 2(n - 1)² + 5(n - 1)
= 2(n² - 2n + 1) + 5n - 5
= 2n² + n - 3
∴​ T_n = (S_n - S_n-1)
​ = (2n² + 5n) - (2n² + n - 3 ) = 4n +3
∴ n^th term, T_n = (4n +3)