# Definition:Term of Sequence

## Definition

The elements of a sequence are known as its terms.

Let $\sequence {x_n}$ be a sequence.

Then the $k$th term of $\sequence {x_n}$ is the ordered pair $\tuple {k, x_k}$.

## Also defined as

Some sources gloss over the fact that a sequence is a mapping and define the terms to be the elements of the range of the sequence:

We call $x_n$ the $n$th term of the sequence.
-- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach: $\S 4.2$

However, this simplistic treatment lacks the precision of the definition provided here, and $\mathsf{Pr} \infty \mathsf{fWiki}$ does not endorse it.

## Also known as

A term of a sequence is referred to in some sources as an element of the sequence.