Question

An arithmetic sequence is represented as 5 , 9 , 13 , ... with the nth term represented as 4n + 1. Write a formula to represent the sum of the first n terms.

Answer 1

Let $a_n=4n+1$.

$S_n=\displaystyle\sum_{k=1}^na_k=\sum_{k=1}^n(4k+1)$
$S_n=\displaystyle4\sum_{k=1}^nk+\sum_{k=1}^n1$
$S_n=\displaystyle4\frac{n(n+1)}2+n$
$S_n=2n^2+3n$