Answer
$a_{n}=20-7n$
$a_{20}=-120$
Work Step by Step
If the sequence is arithmetic, the general rule is
$ a_{n}=a_{1}+(n-1)d\qquad$ ... substitite $n=11$ and $d=-7$
(our goal is to find $a_{1})$
$ a_{11}=a_{1}+(11-1)(-7)\qquad$ ... substitite $a_{11}=-57$, simplify
$-57=a_{1}+(10)(-7)$
$-57=a_{1}-70\qquad$ ... add 70 to both sides
$13=a_{1}$
So, the general rule is
$a_{n}=13+(n-1)(-7)$
$a_{n}=13-7n+7$
$a_{n}=20-7n$
The 20th term is
$a_{20}=20-7(20)=-120$
