Answer
The equation for the $n$th term is
$a_n=13(2)^{n-1}$
and $a_7=832$
Work Step by Step
The given series is
$13,26,52,104,...$
First term $a_1=13$.
Common ratio $r=\frac{26}{13}=2$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $13$ for $a_1$ and $2$ for $r$.
$\Rightarrow a_n=13(2)^{n-1}$
Substitute $7$ for $n$.
$\Rightarrow a_7=13(2)^{7-1}$
Simplify.
$\Rightarrow a_7=13(2)^{6}$
$\Rightarrow a_7=832$.
