Let $\{ a_{n}\}$ be a positive real sequence $a_{n}=\sqrt{a_{n-1}a_{n-2}}$ for $n≥3$, then $\{ a_{n}\}$ converges to $(a_{1}a_{2}^{2})^{1/3}$.
Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$