Definition:Recursive Sequence

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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