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

A. n(n – 2) B. n(n + 2) C. n(n + 1) D. n(n – 1) Answer: Option B
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Solution(By Apex Team)

$\begin{aligned}a_n&=2n+1\\ a_1&=2\times1+1=2+1=3\\ a_2&=2\times2+1=4+1=5\\ \therefore d&=a_2-a_1=5-3=2\\ \therefore S_n&=\frac{n}{2}[2a+(n-1)d]\\ &=\frac{n}{2}[2\times3+(n-1)\times2]\\ &=\frac{n}{2}[6+2n-2]\\ &=\frac{n}{2}[2n+4]\\ &=n[n+2]\end{aligned}$
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