How to Find Recursive Patterns
When you are given a set of numbers to find the recursive pattern for, follow these steps:
1. Find the difference between each of these
numbers.
2. If the differences are the same (Example A) you have found the rule.
If the differences are different (Example B) the next step is to find a pattern to get from one difference to the next each time.
Next take the beginning of the Pattern Rule and apply it to the input to find what else must be done to get the output. This will give you the complete Pattern Rule. |
Example A:
250, 230, 210, 190, 170 250 to 230 = 20, 230 to 210 = 20, 210 to 190 = 20, 190 to 170 = 20 The difference is reducing by 20 each time, so the pattern rule is: Pattern Rule: Start at 250 and subtract 20 each time. Example B: 2, 5, 11, 23, 47 2 to 5 = 3, 5 to 11 = 6, 11 to 23 = 12, 23 to 47 = 24 The differences are 3, 6, 12, 24 To get from one to the next difference you need to multiple each by 2, so the Pattern Rule begins: Start at 2, then multiply by 2. 2 X 2 = 6, need 5 so add 1 5 X 2 = 10, need 11 so add 1 Pattern Rule Start at 2, then multiply by 2 and add 2 to each number. |