sequence

Sequence

A sequence is an indexed family, whose indicies are natural numbers (infinite) $\{1,\dots ,n\}$ (finite).
So sequences are “ordered lists” that may be finite or infinite.
They are most commonly denoted as $(a_1,a_2,a_3,\dots ,a_n)$ or $(a_n{)}_{n=1}^{\infty }=(a_n{)}_{n\ge 1}=(a_k{)}_{k\in \mathbb{N}}$. In context, it could also be denoted $(a_n)$.

Viewed as a function a function:
$x:\mathbb{N}\to X,n\to x_n$
$x:\{1,\dots ,n\}\to X,n\to x_n$.