Answer
$\underline{{{a}_{2}}=\frac{{{\left( -1 \right)}^{2}}}{{{4}^{2}}-1}=\frac{1}{15}}$.
Work Step by Step
Put $n=2$ to get the second term of the sequence given.
Now, to get the third term, put $n=3$ and so on.
We have the general form of the sequence: ${{a}_{n}}=\frac{{{\left( -1 \right)}^{n}}}{{{4}^{n}}-1}$.
So to find the second term, put $n=2$:
$\begin{align}
& {{a}_{2}}=\frac{{{\left( -1 \right)}^{2}}}{{{4}^{2}}-1} \\
& =\frac{1}{16-1} \\
& =\frac{1}{15}
\end{align}$
