Answer
$a_{n}=(-1)^{n+1}\ 5^{n}$
Work Step by Step
We are given:
$5, -25, 125, -625$, ...
We see that the terms in the sequence take on powers of $5$. In addition, we notice that the sign alternates. We find the pattern:
$a_1=(-1)^{2}\ 5^{1}$
$a_2=(-1)^{3}\ 5^{2}$
$a_3=(-1)^{4}\ 5^{3}$
$a_4=(-1)^{5}\ 5^{4}$
...
$a_{n}=(-1)^{n+1}\ 5^{n}$
