Answer
The equation for the $n$th term is
$a_n=4(\frac{5}{2})^{n-1}$
and $a_7=976.5625$
Work Step by Step
The given series is
$4,10,25,62.5,...$
First term $a_1=4$.
Common ratio $r=\frac{10}{4}=\frac{5}{2}$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $4$ for $a_1$ and $\frac{5}{2}$ for $r$.
$\Rightarrow a_n=4(\frac{5}{2})^{n-1}$
Substitute $7$ for $n$.
$\Rightarrow a_7=4(\frac{5}{2})^{7-1}$
Simplify.
$\Rightarrow a_7=4(\frac{5}{2})^{6}$
$\Rightarrow a_7=976.5625$
