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> $ 0so 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.