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  


Create a recursive rule that describes the sequence. Then use the recursive rule to find the odometer's reading the following two weeks, assuming that Bonnie drives exactly the same distance every week.
Before we write the recursive rule for the sequence, let's ensure it's arithmetic.
Notice that Bonnie drives 64 miles each week. Therefore, the odometer readings form an arithmetic sequence with a common difference of d=64. Using d and the given information we can write the recursive rule as follows.