Answer
$n^{2}$
Work Step by Step
$5-3=3-1=2$
there is a constant difference between terms.
The terms of the sum make up an arithmetic sequence, $a_{1}=1, d=2.$
Sum of the First $n$ Terms of an arithmetic sequence:
$S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$
$=\displaystyle \frac{n}{2}(1+(2n-1))$
$=\displaystyle \frac{n}{2}(2n)$
$=n^{2}$