SEAMO 2027 - Paper F - SET 02 - Self-study Question 22

Define $a_0=2$ and $a_n=\dfrac{\sqrt3\,a_{n-1}+1}{\sqrt3-a_{n-1}}$ for $n\ge1$. If $a_{2021}=p+q\sqrt3$ for rational numbers $p,q$, evaluate $|p+q|$.