Answer
$-146$
Work Step by Step
Recall:
The $n^{\text{th}}$ term $a_n$ of an arithmetic sequence is given by the formula
$$a_n=a_1+(n-1)d$$
where
$d$ = common difference
$a_1$ = first term
$n$ = term number
The common difference $d$ of the arithmetic sequence is:
$$d=4-9=-5$$
The given arithmetic sequence has
$a_1=9\\
d=-5\\
n=32$
Use the given values and the formula above to find the $32^{\text{nd}}$ term:
$a_{32}= 9 +(32-1) (-5)\\
a_{32} = 9+(31)(-5)\\
a_{32}=9+(-155)\\
a_{32}=-146$
