Answer
$a_n=(-1)^{n+1}(2n)$
Work Step by Step
The terms, when the signs are ignored, are the multiples of $2$.
This means that the formula for the $n^{th}$ term involves $2n$.
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:
$a_n=(-1)^{n+1}(2n)$
To check:
n=1: $(-1)^{1+1}(2\cdot1) = (-1)^2(2) = 2$
n=2: $(-1)^{2+1}(2\cdot2) = (-1)^3(4) = -4$
n=3: $(-1)^{3+1}(2\cdot3) = (-1)^4(6) = 6$
