$\text { Find the following limit of the sequence as } n \text { approaches infinity, if it exists. }$

$\text { Find the following limit of the sequence as } n \text { approaches infinity, if it exists. }$ $a_{n}=\frac{1}{n}\left(n+\frac{3}{n}\left[\frac{n(n+1) }{5}\right]\right)$

A) $\frac{3}{5}$

B) $\frac{13}{5}$

C) $\frac{8}{5}$

D) $\frac{9}{5}$

E) The limit does not exist.