Question

The sum of the first n terms of an A.P. is 3n² + 6n. Find the n^th term of this A.P.

Answer 1

Given: S_n = 3n₂ + 6n

We know that the nth term of an A.

∴ a_n = S_{n −} S_n−1

S_n−1 = 3(n − 1)² + 6(n − 1)

= 3(n² − 2n + 1) + 6n − 6

= 3n² − 6n + 3 + 6n − 6

= 3n² − 3

∴ a_n = S_{n −} S_n−1

= (3n² + 6n) ₋ (3n² − 3)

= 3n² + 6n − 3n² + 3

= 6n + 3
Thus, n^th term of this A.P. is 6n + 3.