Question

If the sum of first n terms is (3n² + 5n), find its common difference.

Answer 1

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

∴ S_n = 3n² + 5n

\(\Rightarrow\) S_n-1 = 3(n - 1)² + 5(n - 1)

= 3(n² - 2n + 1) + 5(n - 1)

= 3n² - n - 2

Now,

n^th term of AP, a_n = Sn - S_n-1

= (3n² + 5n)-(3n² - n - 2)

= 6n + 2

Let d be the common difference of the AP.

Hence, the common difference of the AP is 6.