Question

The $n^{th}$ term of an $AP$ is $a_n=2n+1$ find its sum.

Answer 1

It is given that,

$a_n=2n+1$

$⟹a_1=3$

And, $Sum=\frac{n}{2}[a_1+a_n]$

$⟹Sum=\frac{n}{2}[3+2n+1]$

$⟹Sum=\frac{n}{2}[4+2n]$

$⟹Sum=n[2+n]$

$⟹Sum=n^2+2n$