Exercise 3 Page 313

To define a sequence recursively, we need a recursive rule. This type of rule gives the beginning term or terms of a sequence, and a recursive equation tells how the $n\text{th}$ term, $a_n,$ is related to one or more preceding terms. For example, let's choose two initial terms. Now, we just need to define a relation that tells us how to obtain the next term from these initial terms chosen. By writing this relation algebraically we obtain the sequence's recursive equation. The relation can be any. For example, the next term is the product of the two previous terms. For this example, this recursive rule defines the recursive sequence shown below.