# Definition:Recursive Sequence

## Definition

A **recursive sequence** is a sequence where each term is defined from earlier terms in the sequence.

A famous example of a recursive sequence is the Fibonacci sequence:

- $F_n = F_{n-1} + F_{n-2}$

The equation which defines this sequence is called a **recurrence relation** or **difference equation**.

### Initial Terms

Let $S$ be a recursive sequence.

In order for $S$ to be defined, it is necessary to define the **initial term** (or terms) explicitly.

For example, in the Fibonacci sequence, the **initial terms** are defined as:

- $F_0 = 0, F_1 = 1$

## Also see

- Inductive Definition of Sequence for the justification of this definition.