Showing that the sequence converges knowing that three other sequences converge I have a question in Analysis. Knowing that $x_{2n}$, $x_{2n-1}$, $x_{3n}$ converge, how can I show that $x_{n}$ converges?

Hint: 1) $x_{2n}$ and $x_{3n}$ should converge to the same limit (by looking at a profitable subsequence of each). 2) A similar argument for another profitable choice of two of $x_{2n}, x_{2n-1}, x_{3n}$. 3) All three given subsequences actually converge to the same limit. We can now conclude via $x_{2n},x_{2n-1}$. 
