Answer
$a_{n}=2^{n}-1$
$a_{6}=63$
$a_{7}=127$
$a_{8}=255$
Work Step by Step
Finding a pattern:
$\left[\begin{array}{llll}
n & a_{n} & & \\
1 & 1 & =2-1 & \\
2 & 3 & =4-1 & =2^{2}-1\\
3 & 7 & =8-1 & =2^{3}-1\\
4 & 15 & =16-1 & =2^{4}-1\\
5 & 31 & =32-1 & =2^{5}-1\\
... & & &
\end{array}\right]$ leading to $a_{n}=2^{n}-1$
For n=6,
$a_{6}=2^{6}-1=64-1=63$
For n=7,
$a_{7}=2^{7}-1=128-1=127$
For n=$8$,
$a_{8}=2^{8}-1=256-1=255$
