The sequence of reals $a_1, a_2, a_3, \ldots$ is defined recursively by the recurrence: $$\dfrac{a_{n+1}}{a_n} - 3 = a_n(a_n - 3)$$Given that $a_{2021} = 2021$, find $a_1$.
Source: OlimphÃada 2021 - Problem 1
Tags: recurrence relation, algebra, Sequence
The sequence of reals $a_1, a_2, a_3, \ldots$ is defined recursively by the recurrence: $$\dfrac{a_{n+1}}{a_n} - 3 = a_n(a_n - 3)$$Given that $a_{2021} = 2021$, find $a_1$.