Simple Patterns Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Simple Patterns.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A repeating pattern is a sequence of elements (colors, shapes, numbers, or sounds) that repeats in a predictable cycle.

Patterns are like the beat of a song—clap-snap-clap-snap repeats over and over. Once you hear the rhythm, you can predict what comes next without looking.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A pattern has a core unit that repeats—once you find it, you can predict and extend the sequence.

Common stuck point: Identifying the core unit when the pattern is longer than two elements (e.g., ABB or ABC patterns).

Sense of Study hint: Cover part of the pattern and try to predict what comes next -- then uncover to check if your rule was correct.

Worked Examples

Example 1

easy
Look at the pattern: circle, square, circle, square, circle, ___. What shape comes next?

Solution

  1. 1
    Identify the repeating unit: circle, square (2-part repeat).
  2. 2
    The pattern so far: circle, square, circle, square, circle.
  3. 3
    After circle comes square.
  4. 4
    The next shape is a square.

Answer

Square
A repeating pattern has a core unit that repeats. Here the core is (circle, square), so after circle always comes square.

Example 2

medium
Find the next two numbers in the pattern: 2, 4, 6, 8, ___, ___.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
What comes next? Red, blue, blue, red, blue, blue, red, ___, ___.

Example 2

medium
Find the next two terms: 5, 10, 15, 20, ___, ___.
← Back to Simple Patterns Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

counting