Question

Choose the correct answer in each of the following questions:

The sum of first n terms of an AP is (4n² + 2n). The nth term of the AP is

(a) (6n − 2) (b) (7n − 3) (c) (8n − 2) (d) (8n + 2) [CBSE 2014]

Answer 1

Let S_n denotes the sum of first n terms of the AP.
$$\begin{gathered} \therefore S_n=4n^2+2n \\ \Rightarrow S_{n-1}=4{\left(n-1\right)}^2+2\left(n-1\right) \\ =4\left(n^2-2n+1\right)+2\left(n-1\right) \\ =4n^2-6n+2 \end{gathered}$$

∴ n^th term of the AP, a_n = S_n − S_{n − 1
$$\begin{gathered} =\left(4n^2+2n\right)-\left(4n^2-6n+2\right) \\ =8n-2 \end{gathered}$$}

Thus, the n^th term of the AP is (8n − 2).

Hence, the correct answer is option C.