Answer
$\dfrac{256}{6561}$
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}=$$\dfrac{2}{3}$ , $n=8$ and $r=\dfrac{4/9}{2/3}=$$\dfrac{2}{3}$:
Substituting these values into the formula ablve gives:
$a_{8}=$ $\dfrac{2}{3}$ $\times$ $\left({\dfrac{2}{3}}\right)^{8-1}$
$a_{8}=$ $\dfrac{2}{3}$ $\times$ $\left({\dfrac{2}{3}}\right)^{7}$
$a_{8}=$ $\dfrac{256}{6561}$
The $8^{\text{th}}$ term is $\dfrac{256}{6561}$.
