Problem

Source:

Tags: Recurrence



Given a sequence of positive integers $$a_1, a_2, a_3, a_4, a_5, \dots$$such that $a_2 > a_1$ and $a_{n+2} = 3a_{n+1} - 2a_n$ for all $n \geq 1$. Prove that $a_{2021} > 2^{2019}$.