In reply to Quentin.

Most children first encounter a recurrence relation in school when arithmetic sequences are introduced. For example, the arithmetic sequence
1, 5, 9, 13, ....
can be described by the recurrence relation
A_{n+1} = A_n + 4
where A_0 = 1.

Geometric sequences also satisfy a simple recurrence relation. For example, the geometric sequence 1, 2, 4, 8, 16,... can be described by the recurrence relation
A_{n+1} = 2*A_n
where A_0 = 1.