CMO 2017 Problem 1

The sequences $\{u_{n}\}$ and $\{v_{n}\}$ are defined by $u_{0} =u_{1} =1$ , $u_{n}=2u_{n-1}-3u_{n-2}$ $(n\geq2)$ , $v_{0} =a, v_{1} =b , v_{2}=c$ , $v_{n}=v_{n-1}-3v_{n-2}+27v_{n-3}$ $(n\geq3)$ . There exists a positive integer $N$ such that when $n> N$ , we have $u_{n}\mid v_{n}$ . Prove that $3a=2b+c$ .