Supersequence (terminology)

If $\displaystyle A \subset B$ with $\displaystyle A, B$ sets then $\displaystyle A$ is a subset, $\displaystyle B$ a superset. My question is, do we use the same terminology for sequences? If $\displaystyle \{x_j\}_{j \in J}$ is a subsequence of $\displaystyle \{x_i\}_{i \in I}$ does that mean that $\displaystyle \{x_i\}_{i \in I}$ is a supersequence?

If not, what do we call it? Surely it must have a name!

Wikipedia thinks supersequence is a geological term, while the Penguin Dictionary of Maths omits both superset and supersequence...