Answer
$-7592$
Work Step by Step
There is a constant difference, $-6$, between terms.
The terms are part of an arithmetic sequence.
nth Term of an Arithmetic Sequence:
$a_{n}=a_{1}+(n-1)d$
$-299=7-6(n-1)\qquad$... solve for n
$-306=-6(n-1)$
$51=(n-1)$
$n=52$
There are $52$ terms in the sum.
The terms of the sum
are the first $52$ terms of an arithmetic sequence, $a_{1}=7, d=-6.$
Sum of the First $n$ Terms of an arithmetic sequence:
$S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$
$S_{52}=\displaystyle \frac{52}{2}\left(7-299\right)=26(-292)=-7592$
