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

Let a be the first term and d be the common difference.

We know that, sum of first n terms = S_n = $\frac{n}{2}$[2a + (n − 1)d]

It is given that sum of the first n terms of an A.P. is 3n² + 6n.

∴ First term = a = S₁ = 3(1)² + 6(1) = 9.

Sum of first two terms = S₂ = 3(2)² + 6(2) = 24.

∴ Second term = S₂ − S₁ = 24 − 9 = 15.

∴ Common difference = d = Second term − First term
= 15 − 9 = 6

Also, n^th term = a_n = a + (n − 1)d
⇒ a_n = 9 + (n − 1)6
⇒ a_n = 9 + 6n − 6
⇒ a_n = 3 + 6n

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