Patterns
Free lessons and practice worksheets for patterns — worked examples, common mistakes, and step-by-step solutions.
- 01Patterns3 min read
Geometric & Numeric Patterns
Geometric and numeric patterns are sequences of numbers that follow predictable rules. An arithmetic sequence maintains a constant difference between consecutive terms, such as 3, 7, 11, 15 where each term increases by 4. A geometric sequence maintains a constant ratio between consecutive terms, such as 2, 6, 18, 54 where each term is multiplied by 3.
- 02Patterns3 min read
Growing Patterns
A growing pattern is a sequence of numbers that increases according to a specific rule, where each term builds upon the previous ones in a predictable way. These patterns can follow simple arithmetic progressions like 2, 4, 6, 8 (adding 2 each time) or more complex structures like triangular numbers 1, 3, 6, 10, 15 (where differences increase by 1). Identifying the underlying rule allows mathematicians to predict any term in the sequence without calculating all preceding values.
- 03Patterns3 min read
Repeating Patterns
A repeating pattern is a sequence where the same group of elements appears continuously in the same order. The smallest group that creates the pattern is called the repeating unit or cycle. For example, in the sequence A, B, C, A, B, C, A, B, C, the repeating unit is A, B, C with a cycle length of 3.