**Definition:** A sequence is an ordered list of infinitely many numbers indexed by the natural numbers \(1, 2, 3, \ldots\)

Equivalently, a sequence is a function \(a(n)\) whose domain is the natural numbers \(\mathbb{N}\). We usually write \(a_n\) for the \(n\)th term in the sequence and use \(\lbrace a_n \rbrace\) to represent the entire sequence.

\(1, 4, 9, 16, 25, \ldots\)

\(-1, +1, -1, +1, -1, \ldots\)

\(1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots\)

\(1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \ldots\)