Question

If the $n^{th}$ term of an A.P. is $(2n+1)$, find the sum of first $n$ terms of the A.P.

Answer 1

We have,
$a_n=(2n+1)⟹a_1=2\times 1+1=3$

So, the given sequence is an A.P. with first term $a=a_1=3$ and last term $l=a_n=2n+1$.

Therefore, the sum of $n$ terms is given by
$S_n=\frac{n}{2}(a+l)=\frac{n}{2}\{3+(2n+1\left)\right\}=\frac{n}{2}(2n+4)=n(n+2)$