# A recursive sequence (2)

Algebra Level 3

$\large \begin{cases} a_1=2017\\ a_2=2117\\ a_{n+2}=\frac{2}{5}a_{n+1}+\frac{3}{5}a_n, \quad n\ge 1. \end{cases}$

Let $$\left \{a_n\right \}$$ be a sequence satisfying the above condition. Find $$\displaystyle \lim_{n \to \infty } a_n$$.

×