Answer
$-\dfrac{3}{2048}$
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:
$a_{1}=24$ , $n=8$ and $r=\dfrac{-6}{24}=\dfrac{-1}{4}$:
Substituting these values into the formula above gives:
$a_{8}=$ $24$ $\times$ $\left(-\dfrac{1}{4}\right)^{8-1}$
$a_{8}=$ $24$ $\times$ $\left(-\dfrac{1}{4}\right)^{7}$
$a_{8}=$ $-\dfrac{3}{2048}$
The $8^{\text{th}}$ term is $-\dfrac{3}{2048}$.
