Recursive Models

Another way to represent an arithmetic sequence is a **recursive function**, or any model that demonstrates how to find the next term in a sequence. In order to find the next term, *a _{n}*, add the common difference to the previous term,

**Example** Write a recursive function to model the following sequence:

-3, -1, 1, 3, 5 …

*Step 1. *Determine the common difference.

-1 - (-3) = 2

1 - (-1) = 2

The common difference is two, *d* = 2.

*Step 2. *Write a recursive model and reference the first term.

*a _{1 = }-3*

*a _{n} = a_{n -1 }+ 2 *