Answer
The equation for the $n$th term is
$a_n=(4)^{n-1}$
and $a_9=65536$
Work Step by Step
The given series is
$1,4,16,64,...$
First term $a_1=1$.
Common ratio $r=\frac{4}{1}=4$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $1$ for $a_1$ and $4$ for $r$.
$\Rightarrow a_n=1(4)^{n-1}$
$\Rightarrow a_n=(4)^{n-1}$
Substitute $9$ for $n$.
$\Rightarrow a_9=(4)^{9-1}$
Simplify.
$\Rightarrow a_9=(4)^{8}$
$\Rightarrow a_9=65536$.
