The question is:

Prove that the sequence is monotone and bounded. Then find the limit.

$\displaystyle s_{1}$=1 and $\displaystyle s_{n+1}$=$\displaystyle \frac{1}{4}$($\displaystyle s_{n}$+5)for n $\displaystyle \in$ N.

{$\displaystyle s_{n}$} is increasing.

Are we guessing that $\displaystyle s_{n}$ $\displaystyle \leq 2$?