Determine if the sequence $\{a_n\}$ converges, when

$a_n=8cos(\frac{2n+8}{6n+6}),$

and if it does, find its limit$.$

limit $=8cos(\frac{4}{3})$

$\underset{?}{lim}it=cos(\frac{4}{3})$

$\underset{?}{lim}it=4\sqrt[\phantom{2}]{3}$

$4.$ sequence does not converge

limit $=\frac{8}{3}$

$\underset{?}{lim}it=4$