A recursive rule gives the first term or terms of a sequence and describes how each term is related to the preceding term(s) with a recursive equation. For example, arithmetic and geometric sequences can be described recursively.

Example arithmetic sequence	Example geometric sequence
Recursive equation
$$\begin{array}{c}{a}_1=3,a_n=a_{n-1}+2\end{array}$$	$$\begin{array}{c}{a}_1=5,a_n=a_{n-1}\times 2\end{array}$$

One particularly well-known sequence that is defined recursively is the Fibonacci sequence, in which each term is the sum of the two previous terms.