The terms $a_1,a_2,a_3,...\hspace{0.5em}{a}_n,...\hspace{0.5em}$ of a sequence are given by:

${\displaystyle a_n=\frac{1+a_{n-1}}{a_{n-2}}.}$

Investigate the sequences you get when you choose your own first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture? Investigate the sequences.