Q: Let $\displaystyle x\in{O}$, where $\displaystyle O$ is an open set. If $\displaystyle (x_{n})$ is a sequence converging to x, prove that all but a finite number of the terms of $\displaystyle (x_{n})$ must be contained in $\displaystyle O$.

I am not sure where to begin with for this proof. Looking at it, i'd assume we need to use the definition of a cluster (limit point) somewhere in the proof. However, I am not sure. I am having a trouble breaking down the statement, so that I know what my goal really is.