Answer
$a_{n}=\displaystyle \frac{(-1)^{n+1}}{n^{2}}$
Work Step by Step
The sign alternates, so there will be $(-1)^{k}$ in the general expression.
The even n's have a minus sign so
we will have $(-1)^{n+1}$ in the expression for the n-th term.
The denominators of the terms are for
first term, the square of 1
second term, the square of 2, etc
...
n-th term, the square of n.
so, the n-th term will have $(-1)^{n+1}$ to determine its sign , and
$\displaystyle \frac{1}{n^{2}}$ for the magnitude:
$a_{n}=\displaystyle \frac{(-1)^{n+1}}{n^{2}}$
