Answer
The equation for the $n$th term is
$a_n=2(4)^{n-1}$
and $a_6=2048$
Work Step by Step
The given series is
$2,8,32,128,...$
First term $a_1=2$.
Common ratio $r=\frac{8}{2}=4$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $2$ for $a_1$ and $4$ for $r$.
$\Rightarrow a_n=2(4)^{n-1}$
Substitute $6$ for $n$.
$\Rightarrow a_6=2(4)^{6-1}$
Simplify.
$\Rightarrow a_6=2(4)^{5}$
$\Rightarrow a_6=2048$.
