Question

The sum of the first n terms of an A.P. is 4n² + 2n. 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 4n² + 2n.

∴ First term = a = S₁ = 4(1)² + 2(1) = 6.

Sum of first two terms = S₂ = 4(2)² + 2(2) = 20.

∴ Second term = S₂ − S₁ = 20 − 6 = 14.

∴ Common difference = d = Second term − First term
= 14 − 6 = 8

Also, n^th term = a_n = a + (n − 1)d
⇒ a_n = 6 + (n − 1)(8)
⇒ a_n = 6 + 8n − 8
⇒ a_n = 8n − 2

Thus, n^th term of this A.P. is 8n − 2.