Patterns in Math — Definition, Formula & Examples
Patterns in math are sequences of numbers, shapes, or objects that follow a predictable rule. Recognizing a pattern means figuring out what comes next by identifying the rule that connects each item to the one before it.
A mathematical pattern is an ordered set of elements (numbers, geometric figures, or expressions) in which each successive element is related to the previous one by a consistent rule or operation.
How It Works
To find a pattern, look at how each item changes from one step to the next. Ask yourself: is a number being added, subtracted, multiplied, or divided each time? Once you identify the rule, you can predict the next items in the sequence. For shape patterns, look for repeating groups of shapes or rotations. Writing out the differences between consecutive terms is one of the easiest ways to spot a number pattern.
Worked Example
Problem: Find the next two numbers in the pattern: 3, 7, 11, 15, ___, ___
Find the rule: Subtract each number from the one after it to see what changes.
Apply the rule: Each term is 4 more than the previous term. Add 4 to continue the pattern.
Answer: The next two numbers are 19 and 23.
Why It Matters
Spotting patterns is the foundation of algebra — every equation like describes a pattern. Scientists use patterns to make predictions, and computer programmers rely on patterns when writing loops and algorithms.
Common Mistakes
Mistake: Assuming the pattern always uses addition when it might use multiplication or another operation.
Correction: Always check the differences AND the ratios between consecutive terms. For example, 2, 6, 18, 54 grows by multiplying by 3, not by adding.