What is a sequence?

A sequence is simply an ordered list of numbers arranged according to a certain pattern or rule. Each number in the sequence is called a term, and we usually label these terms as u1​,u2​,u3​,,un​,…. The number un​ is known as the nth term of the sequence.

For example, consider these sequences:

• Sequence A: 2,4,6,8,10,…

• Sequence B: 1,21​,41​,81​,…

• Sequence C: 3,−1,4,−1,5,…

Sequences can have various behaviors:

• They might increase, decrease, alternate, or approach a specific value.

• They can be described explicitly (with a clear formula for each term) or recursively (each term defined in relation to previous ones).

Understanding the general idea of sequences prepares us for learning special kinds of sequences, like arithmetic and geometric sequences, each of which follows specific and interesting rules.