Answer
$a_n=(-1)^{n+1}(n)$
Work Step by Step
The terms, when the signs are ignored, are the whole numbers.
This means that the formula for the $n^{th}$ term involves $n$.
The sign of the terms alternate, starting with positive.
This means that the formula for the $n^{th}$ term involves a power of $-1$.
Since the first term is positive, the exponent/power of $-1$ is either $n+1$ or $n-1$.
If $n+1$ is used, the formula for the $n^{th}$ term is:
$a_n=(-1)^{n+1}(n)$
To check:
n=1: $(-1)^{1+1}(1) = (-1)^2(1) = 1$
n=2: $(-1)^{2+1}(2) = (-1)^3(2) = -2$
n=3: $(-1)^{3+1}(3) = (-1)^4(3) = 3$