Question 181
Determine all periodic sequences $x_{1}, x_{2}, x_{3}, \ldots$ of positive real numbers such that for all $n \geq 1$
$$
x_{n+2}=\frac{1}{2}\left(\frac{1}{x_{n+1}}+x_{n}\right)
$$
$$
x_{n+2}=\frac{1}{2}\left(\frac{1}{x_{n+1}}+x_{n}\right)
$$