Answer
$n(7+2n)$
Work Step by Step
$a_3-a_2=17-13=a_2-a_1=13-9=4=d$, thus this is an arithmetic sequence with a common difference of $4$.
The nth term of an arithmetic sequence can be obtained by the following formula: $a_n=a_1+(n-1)d$, where $a_1$ is the first term and $d$ is the common difference.
The sum of the first $n$ terms of an arithmetic sequence can be obtained by the following formula: $\frac{n(a_1+a_n)}{2},$ where $a_1$ is the first term, $a_n$ is the nth term and $n$ is the number of terms.
Thus the sum:$\frac{n(a_1+a_n)}{2}=\frac{n(a_1+a_1+(n-1)d)}{2}=\frac{n(9+9+(n-1)4)}{2}=\frac{n(18+4n-4)}{2}=\frac{n(14+4n)}{2}=n(7+2n)$
