Prove that $x_n$ converge if subsequences $(x_{2n})$, $(x_{2n+1})$ and $(x_{3n})$ converge
Let $\{x_n\}$ be a sequence in a metric space such that $\{x_{2n}\}$, $\{x_{2n+1}\}$ and $\{x_{3n}\}$ all convergent. Show that $\{x_{n}\}$ converges