Answer
$S_{50}=6,600$
Work Step by Step
RECALL:
(1) The sum of the first $n$ terms, $s_n$, of an arithmetic sequence can be found using the formula
$S_n = \frac{n}{2}(a_1+a_n)$
where
$a_1$=first term
$a_n$ = $n^{th}$ term
(2) The $n^{th}$ term, $a_n$, of an arithmetic sequence can be found using the formula
$a_n=a_1 + d(n-1)$
where
$d$=common difference
$a_1$ = first term
To find the sum of the first 50 terms of the sequence, we need to find the value of $a_{50}$. However, the value of $a_{50}$ can only be found if we know the value of $d$.
Solve for $d$ by subtracting the first term to the second term to obtain:
$d=-9-(-15)
\\d=-9+15
\\d=6$
The first term of the sequence is $-15$ so $a_1=-15$.
Substitute these values into the formula in (2) above to obtain;
$a_n= -15+6(n-1)$
Solve for the 50th term of the sequence to obtain:
$a_{50} = -15 + 6(50-1)
\\a_{50} = -15+ 6(49)
\\a_{50} = -15 + 294
\\a_{50} = 279$
Solve for the sum of the first 50 terms using the formula in (1) above to obtain:
$S_{50} = \frac{50}{2}(-15+279)
\\S_{50} = 25(264)
\\S_{50} = 6,600$
