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, an, add the common difference to the previous term, an-1. An example of a recursive model is: an = an-1 + d. This formula is also known as the recursive formula and is used when previous terms and the common difference are known values.

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.

a1 = -3

an = an -1 + 2