Recursive
Formulas
Example 3
Find the recursive formula given the following table:
In this example, the initial term is the 0 term, not 1. Most of the time, recursive formulas begin with either term 0 or 1. There are other ways to show the initial term including 
for the zero term or 
for the first term. Other letters may be used as well. In this case, 
.
Now find the pattern in the table. From one term to the next, a constant amount is not added but multiplied.
In this case, to go from one term to the next, multiply by 3. Therefore, the recursive formula is:
;