Answer
$\frac{1}{5},-\frac{1}{25},\frac{1}{125},-\frac{1}{625}, \frac{1}{3125}$
Work Step by Step
To find the first five terms of the sequence $a_n = \frac{(-1)^{(n-1)} }{5^n}$, we must plug in $n=1, n=2, n=3, n=4,$ and $n=5.$
$a_1 = \frac{(-1)^{(1-1)} }{5^1}=\frac{1}{5}$
$a_2 = \frac{(-1)^{(2-1)} }{5^2}=-\frac{1}{25}$
$a_3 = \frac{(-1)^{(3-1)} }{5^3}=\frac{1}{125}$
$a_4 = \frac{(-1)^{(4-1)} }{5^4}=-\frac{1}{625}$
$a_5 = \frac{(-1)^{(5-1)} }{5^5}=\frac{1}{3125}$
Hence we see that the first five terms are $\frac{1}{5},-\frac{1}{25},\frac{1}{125},-\frac{1}{625}, \frac{1}{3125}$
