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A sequence in mathematics is an enumerated collection of objects in which repetitions are allowed and order matters. It is often thought of as a list of numbers, but in fact, the objects can be anything: numbers, functions, sets, geometric shapes, or even other sequences.

The elements of a sequence are called terms. The order in which the terms appear is significant, so a sequence is not the same as a set. For example, the sequence (1, 2, 3) is different from the sequence (3, 2, 1). Sequences can be finite, meaning they have a limited number of terms, or infinite, continuing without end.

Sequences are commonly denoted using subscripts, such as $a_n$ for the nth term of a sequence $a$. The entire sequence is often represented by $(a_n)$ or $\{a_n\}$. For instance, a common sequence is the sequence of natural numbers, which can be written as $(1, 2, 3, 4, ...)$ or $(n)_{n \in \mathbb{N}}$.

There are many types of sequences, including arithmetic sequences (where the difference between consecutive terms is constant) and geometric sequences (where the ratio between consecutive terms is constant). Sequences are fundamental in various areas of mathematics, including calculus, discrete mathematics, and computer science, where they are used to model processes, define functions, and construct more complex mathematical objects.