Clearly an explicit definition is more convenient in this way. However, many sequences are much more easily defined by recursive definitions. Here is an example of the Fibonacci numbers. One of our goals is to take recursively defined sequences, or recurrences, and find explicit definitions for the same sequence. Maple has a specific command, rsolve, to solve recurrences.
Lets see how it works.
Here is the recursive definition of a sequence, followed by the rslove command. The final command, seq, is a way of then evaluting this function to find the first 20 elements of the sequence. Many of these sequences have more complicated formulas. The method is essentially the same. One difference is that there needs to be two seed values to start the process.