Answer
$a_{n}=(-1)^{n+1}\times\frac{n^{2}}{n+1}$
Work Step by Step
{${\frac{1}{2}, -\frac{4}{3}, \frac{9}{4}, -\frac{16}{5}, \frac{25}{6}}$}
The first few terms switch between positive and negative so,
$a_{n}=(-1)^{n+1}$
We then notice that the numerator exponentially increases as the denominator increases by one each term.
Numerator: ${n^{2}}$
Denominator: $n+1$
Combine all three equations and we get,
$a_{n}=(-1)^{n+1}\times\frac{n^{2}}{n+1}$
