## Algebra 2 (1st Edition)

$a_{n}=2^{n}-1$ $a_{6}=63$ $a_{7}=127$ $a_{8}=255$
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=$8$, $a_{8}=2^{8}-1=256-1=255$