Answer
The series diverges because $r=\dfrac{3}{2}$.
Work Step by Step
RECALL:
(1)
The common ratio $r$ of a geometric sequence is equal to the quotient of any term and the term before it.
$r=\dfrac{a_n}{a_{n-1}}$
(2)
A geometric series converges if $|r| \lt 1$. The sum of a convergent infinite geometric series is given by the formula:
$S_{\infty}=\dfrac{a_1}{1-r}$
where
$r$ = common ratio
$a_1$ = first term
$\bf\text{Solve for r}:$
$r=\dfrac{a_2}{a_1} = \dfrac{12}{8}=\dfrac{3}{2}$
Since $|\frac{3}{2}|=\frac{3}{2} \not\lt 1$, the infinite geometric series diverges.
