#### Answer

$n=25$

#### Work Step by Step

For an arithmetic series, the sum for the finite series is given by:
$S_n=\dfrac{n(a_1+a_n)}{2}$
We are given that $S_n=-1150$
Now,
$-1150=\dfrac{n \times (50+58-8n)}{2}$
or, $2n^2-27n-575=0$
or, $(n-25) (2n+23)=0$
This gives: $n=25, \dfrac{-23}{2}$
Hence, the positive solution for $n$ is $n=25$