# Real Analysis – Sequence with \$ x_ {n + 2} = x_ {n + 1} x_n \$

Let $$(x_n) _n ge 0$$ to be a sequence for that $$x_ {n + 2} = x_ {n + 1} x_n$$,$$x_0 = a, x_1 = b$$, $$a, b in mathbb {R}$$. To study the monotony and convergence of $$(x_n) _n ge 0$$.
I think I have to study the monotony and the convergence according to the values ​​of $$a$$ and $$b$$. What I've observed is that if $$a, b> 0$$so I can apply $$ln$$ on the recurrence relation and find an explicit formula for $$x_n$$. If any of them is $$0$$,then $$x_n = 0, forall n in mathbb {N}$$. I stay with the cases when they are both negative, when one of them is negative and the other is positive. I do not know what to do to solve them.