Question

The sum of the first n terms of an AP is (3n² + 6n). Find the nth term and the 15th term of this AP.

Answer 1

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

∴ S_n = 3n² + 6n

⇒ `S_(n - 1) = 3(n - 1)^2 + 6(n - 1)`

= 3(n² – 2n + 1) + 6(n – 1) 

= 3n² – 3

∴ n^th term of the AP,

a_n = S_n – S_n–1 

= (3n² + 6n) – (3n² – 3)

= 6n + 3 

Putting n = 15, we get

a₁₅ = 6 × 15 + 3

= 90 + 3

= 93

Hence, the n^th term is (6n + 3) and 15^th term is 93.