Given a metric space $X$ which is sequentially compact (i.e every sequence has a converging subsequence), show that $X$ is complete and totally bounded.
I've already shown that $X$ is complete, since given $(x_n)$ a Cauchy sequence in $X$, there exist a converging subsequence $x_{n_{k}} \to x \in X$ which implies $x_n \to x$ (I have already proven this result previously). However when trying to prove that it is totally bounded, Im finding it quite difficult, since I don't know what strategy to take to write in some way, my space $X$ in terms of sequences to therefore use my hypothesis. Any hint?