Let $(M,d)$ be a Metric Space and Let $X:\mathbb N \to M$ be a converegent sequence to $l \in M$

Prove that $H = \{X\_n\}^\infty\_{n = 1}\cup \{l\}$ is compact by sequences

I know that to prove that a set is compact by sequences, then we need that every sequences admits a convergente subsequence, and I know that the Heine Borel theorem is not applicable for all metric spaces. How should I proceed then?