Sequences

A sequence is a function whose domain is the set of positive integers (or sometimes non-negative integers), and whose values are numbers. The $n$th term of a sequence is usually written as $a_n$, where $n$ is the position in the sequence.

Important properties

• A sequence can be finite or infinite.

• The general term $a_n$ can often be given by a formula or a rule.

• Sequences can be defined explicitly (by a formula for $a_n$) or recursively (each term depends on previous terms).

• The order of terms is important: $(2, 4, 6)$ is different from $(4, 2, 6)$.