## College Algebra 7th Edition

$a_{n}=(-1)^{n+1}\ 5^{n}$
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: $a_1=(-1)^{2}\ 5^{1}$ $a_2=(-1)^{3}\ 5^{2}$ $a_3=(-1)^{4}\ 5^{3}$ $a_4=(-1)^{5}\ 5^{4}$ ... $a_{n}=(-1)^{n+1}\ 5^{n}$