Sequences with recurrence relations

The sequence $(x_n)$ of positive real numbers satisfies the relationship $x_{n-1} \cdot x_n \cdot x_{n+1} = 1$ for all $n \geq 2$.

Given $x_1 = 1$ and $x_2 = 2$, what are the values of the next few terms? What can you say about the sequence? What happens for other starting values?

Part 2. The sequence $(y_n)$ satisfies the relationship $y_{n-1} \cdot y_{n+1} + y_n = 1$ for all $n \geq 2$. Given $y_1 = 1$ and $y_2 = 2$, what are the values of the next few terms? What can you say about the sequence? What happens for other starting values?