Recursive
Formulas
Recursion is the process of choosing a starting term and repeatedly applying the same process to each term to arrive at the following term. Recursion requires that you know the value of the term immediately before the term you are trying to find.
A recursive sequenceis an ordered list of numbers defined by a starting value and a rule. Given a list of numbers when the same operation is applied over and over, a formula or rule can be written. A recursive formula always has two parts:
- The starting value which is called
. This means the first term in the list or the function rule for term one. - The recursion equation or formula which states what operation is being done to the previous term, called
, to get to any term known as 
.
The recursive formula for the ordered list 1,3,5,7,9, . . . would be:
