Answer
$0.0018310546875$
Work Step by Step
Recall the formula for the $n^{\text{th}}$ term of a geometric sequence:
$a_{n}=$ $a_{1}$ $\times$ $r^{n-1}$
where
$a_n$ = $n^{\text{th}}$ term;
$a_1$ = first term;
$n$ = term number'
$r$ = common ratio
The given geometric sequence has:
$a_{1}=-30$ , $n=8$ and $r=\dfrac{7.5}{-30}=-0.25$:
Substituting these values into the formula above gives:
$a_{8}=$ $-30$ $\times$ $(-0.25)^{8-1}$
$a_{8}=$ $-30$ $\times$ $(-0.25)^{7}$
$a_{8}=0.0018310546875$
The $8^{\text{th}}$ term is $0.0018310546875$.
