If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is

Answer: Option B

$$\begin{array}{rl}& a_n=2n+1\\ & a_1=2\times 1+1=2+1=3\\ & a_2=2\times 2+1=4+1=5\\ & \therefore d=a_2-a_1=5-3=2\\ & \therefore S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]\\ & =\frac{n}{2}\left[2\times 3+\left(n-1\right)\times 2\right]\\ & =\frac{n}{2}\left[6+2n-2\right]\\ & =\frac{n}{2}\left[2n+4\right]\\ & =n\left[n+2\right]\end{array}$$