Answer
$a_{n}=n^{(-1)^{n+1}}$
Work Step by Step
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:
$a_{n}=n^{(-1)^{n+1}}$
