what is sequence

In mathematics, a sequence is an ordered list of objects, usually numbers, in which repetitions are allowed and order matters. A sequence can be thought of as a list of elements with a particular order. The number of elements in a sequence is called its length. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. There are different types of sequences, including finite and infinite sequences. In a finite sequence, there is a specific number of terms, while in an infinite sequence, it continues indefinitely. Sequences can be described in different ways, such as an explicit formula, a recurrence relation, or a table of values. Sequences are also the basis for series, which are important in differential equations and analysis.