Sequence

A sequence is a list of objects, potentially finite or infinite.

In Maths Index for a finite sequence of length $n$ this will be denotes by

$$a_1, a_2, \ldots a_n$$

which secretly is a function

$$a: [1,n] \rightarrow D$$

where $D$ is your domain of interest.

However for 1 way finite sequences we use

$$a_1, a_2, \ldots, a_n, \ldots$$

or $a: \mathbb{N} \rightarrow D$. For 2 way infinite sequence we would use

$$\ldots, a_{-n}, \ldots, a_{-1}, a_0, a_1 \ldots, a_n, \ldots$$

or $a: \mathbb{Z} \rightarrow D$.

When I say $D$ just think of the Integers $\mathbb{Z}$ so such a sequence could be

$$ 5, 7, 4, -3, 9, 1, 10, 4, 5, 8, 9, 3 $$