## College Algebra 7th Edition

$a_{n}=n^{(-1)^{n+1}}$
We are given: $1, \frac{1}{2}, 3, \frac{1}{4}, 5, \frac{1}{6}$ ... We notice that the terms are integers raised to positive or negative $1$ (alternating). We find the pattern: $a_1=1^1$ $a_2=2^{-1}$ $a_3=3^{1}$ $a_4=4^{-1}$ $a_5=5^{1}$ Therefore: $a_{n}=n^{(-1)^{n+1}}$