Answer
The equation for the $n$th term is
$a_n=(-5)^{n-1}$
and $a_7=15625$
Work Step by Step
The given series is
$1,-5,25,-125,...$
First term $a_1=1$.
Common ratio $r=\frac{-5}{1}=-5$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $1$ for $a_1$ and $-5$ for $r$.
$\Rightarrow a_n=1(-5)^{n-1}$
$\Rightarrow a_n=(-5)^{n-1}$
Substitute $7$ for $n$.
$\Rightarrow a_7=(-5)^{7-1}$
Simplify.
$\Rightarrow a_7=(-5)^{6}$
$\Rightarrow a_7=15625$.
