#### Answer

$S_{20}=1020$

#### Work Step by Step

RECALL:
(1) The sum of the first $n$ terms of an arithmetic sequence is given by the formula:
$S_n=\dfrac{n}{2}(a+a_n)$
where
$a$ = first term
$d$ = common difference
$a_n$ = $n^{th}$ term
(2) The $n^{th}$ term $a_n$ of an arithmetic sequence is given by the formula:
$a_n = a + (n-1)d$
where
$a$ = first term
$d$ = common difference
The given arithmetic sequence has:
$a=89
\\a_n = 13
\\d=85-89=-4$
The formula for the partial sum requires the values of $a$, $a_n$ and $n$.
However, only $a$ and $a_n$ are known at the moment.
Solve for $n$ using the formula for $a_n$ to obtain:
$\require{cancel}
a_n = a + (n-1)d
\\13 = 89+(n-1)(-4)
\\13-89 = (n-1)(-4)
\\-76=(n-1)(-4)
\dfrac{-76}{-4}=\dfrac{(n-1)(-4)}{-4}
\\19=n-1
\\19+1=n-1+1
\\20=n$
Now that it is known that $n=20$, the sum of the first 20 terms can be computed using the formula above.
$S_{20} = \dfrac{20}{2}(89+13)
\\S_{20}=10(102)
\\S_{20}=1020$