Math 1 · Unit 9 · Lesson 4 · part 4 of 5
When each rule is handier
If both rules describe the same list, why keep two?
When each rule is handier
If both rules describe the same list, why keep two? Because each is handier for a different job.
Recursive is easy to readIt says in one glance how the list moves: add 12, or multiply by 3. It is good for the next few terms, and it is how a spreadsheet fills down a column.
Explicit is the elevatorIt finds the 100th term without working out the 99 before it. It is what you want for a far term, or for finding which term has a certain value.
Feel the difference. Find the 40th term of an + 1 = an + 12, a1 = 4, first by the stairs and then by the elevator.
Why know both? The Fibonacci numbers0, 1, 1, 2, 3, 5, 8, 13, ... Each term is the sum of the two before it. As a recursive rule that is short: a1 = 0, a2 = 1, and an = an − 1 + an − 2. But there is no easy explicit rule for it at our level: to get the 30th Fibonacci number you really do climb the stairs. Some lists are natural one way and hard the other, which is a good reason to be able to read and write both kinds of rule.