## Calculus 8th Edition

$a_n = -\frac{(-1)^nn^2}{n+1}$
Our first term is $a_1 = \frac{1}{2}$. The sequence alternates, so we have a factor of $(-1)^n$. We observe that we are also multiplying by $\frac{n^2}{n+1}$ each term. Since $a_1 = \frac{1}{2}$, we must have $$a_n = -\frac{(-1)^nn^2}{n+1}.$$