finding a sequence that diverges

let $a_n$ be a sequence where for all $n\ge3$$a_n \in (a_{n-1},a_{n-2})$ or $a_n \in (a_{n-2},a_{n-1})$

i need to find an example to such sequence that diverges.

i figured that such sequence is of the form of somthing like $a_n = \dfrac{a_{n-1} - a_{n-2}} n + somthing$

not sure how to go from here.