Australian AMC 2024 - Senior Question 28

The sequence $a_1,a_2,a_3,\ldots$ starts with an integer $a_1$ and satisfies $a_{n+1}=\dfrac{3a_n-1}{a_n+1}$ for every positive integer $n$. The 33rd term is $a_{33}=\dfrac{2024}{1905}$. What is $a_1$, the first term of the sequence?