What Are Recursive Sequences?

A recursive sequence is an ordered set of numbers where the first items are called starting values and all other terms can be computed recursively from the starting values. Recursion means to apply a formula repeatedly to compute a sequence term using the values before it.

A recursive sequence can have one or more starting values. Geometric sequences, for example, start with a value such as one, after which all other terms are obtained by multiplying the previous term by a specific number. Arithmetic sequences are similar, but they rely on addition instead of multiplication. The Fibonacci numbers are a famous recursive sequence with two starting values, zero and one. Every other term is computed by adding the two terms that precede it.