A sequence is an ordered listing of numbers such as {1, 3, 5, 7, 9}. In mathematical terms, a sequence is a function whose domain is the natural number set {1, 2, 3, 4, 5, …}, or some subset of the natural numbers, and whose range is the set of real numbers or some subset thereof. Let f denote the sequence {1, 3, 5, 7, 9}. Then f(1) = 1, f(2) = 3, f(3) = 5, f(4) = 7, and f(5) = 9. Here the domain of f is {1, 2, 3, 4, 5} and the range is {1, 3, 5, 7, 9}.

The terms of a sequence are often designated by subscripted variables. So for the sequence {1, 3, 5, 7, 9}, one could write a₁ = 1, a₂ = 3, a₃ = 5, a₄ = 7, and a₅ = 9. A shorthand designation for a sequence written in this way is {a_n}. It is sometimes possible to get an explicit formula for the general term of a sequence. For example, the general nth term of the sequence {1, 3, 5, 7, 9} may be written a_n = 2n -1, where n takes on values from the set...