Answer
$-500$
Work Step by Step
Sum of first $n$th term of an arithmetic sequence can be calculated as:
$S_n=\dfrac{n}{2}[a_1+a_n]$
since, we have {$4,2,0,...., -44$}
This implies that $a_1=4,a_n=-44,n=25$
Now,
$S_{25}=\dfrac{25}{2}[4+(-44)]=-500$