Answer
$\{a_n\}=2n \ (-1)^{n+1}$
Work Step by Step
We that the sequence starts from $2$ and the alternates the sign with each new term.
Aside from the sign change, the value gets multiplied by $2$ with each new term. So, we determine the pattern as:
$\{a_n\}=2n \ (-1)^{n+1}$
