Number Patterns and Pattern Rules

A Number Pattern:

A list of numbers that follow a certain sequence or pattern.

They can be ascending or descending.

Pattern Rule: How a pattern grows or changes.

Types of Pattern Rules:

A Recursive Pattern Rule: is a pattern rule that tells you the start number of a pattern and how the pattern continues. For example, a recursive rule for the pattern 5, 8, 11, 14, … is start with 5 and add 3.

A Common Difference: is the difference between any two consecutive terms in a pattern. Not all patterns have a common difference. For example, the pattern 5, 10, 15, 20, … has a common difference of 5. The pattern 1, 4, 9, 16, … has no common difference.

An Explicit Pattern Rule: is a pattern rule that tells you how to get any term in the pattern without listing all the terms before it. For example, an explicit pattern rule for 5, 8, 11, 14, … uses the first term (5) and the common difference (3). To calculate the 20th term, 20th term first term  [(term number 1) (common difference)] 5 (19 3) 5 57 62