Answer
{$\frac{1}{5}$, $-\frac{1}{25}$, $\frac{1}{125}$, $-\frac{1}{625}$, $\frac{1}{3125}$}
Work Step by Step
Plug in $n = 1:$
$a_1 =$ $\frac{(-1)^0}{5^1}$ $= $$\frac{1}{5}$
Plug in $n=2:$
$a_2 = $ $\frac{(-1)^{2-1}}{5^2}$ $= $$-\frac{1}{25}$
Doing the same for $n = 3, 4, 5$, we obtain
$a_3 = $ $\frac{1}{125}$
$a_4 = $ $-\frac{1}{625}$
$a_5 = $ $\frac{1}{3125}$
And so, the first five terms of the sequence are $:$
{$\frac{1}{5}$, $-\frac{1}{25}$, $\frac{1}{125}$, $-\frac{1}{625}$, $\frac{1}{3125}$}
