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 simple pattern repeats a fixed core unit (like AB or ABB) over and over, so the next element is whatever the cycle says comes next.

Common stuck point: The procedure for simple patterns is the easy part; the trap is looking only at the last element to predict next. Asking "Does a fixed chunk repeat unchanged so I can predict by the cycle?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does a fixed chunk repeat unchanged so I can predict by the cycle?

Worked Examples

Example 1

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

Answer

Square

First step

1
Identify the repeating unit: circle, square (2-part repeat).

Full solution

  1. 2
    The pattern so far: circle, square, circle, square, circle.
  2. 3
    After circle comes square.
  3. 4
    The next shape is a 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, ___, ___.

Example 3

easy
You see a pattern: clap, stomp, clap, stomp, clap, ___. What do you do next?

Example 4

medium
Pat the pattern: up, down, up, down, up, ___. What is next?

Example 5

medium
You see socks on a line: pink, white, pink, white, pink, white, ___. What color is next?

Example 6

easy
Find the next two terms: circle, circle, square, circle, circle, square, ___, ___.

Example 7

medium
A bracelet has beads: green, white, purple, green, white, purple. What two beads come next?

Example 8

medium
A clap pattern goes: clap, clap, snap, clap, clap, snap, clap, ___, ___.

Example 9

easy
A piggy bank holds 10,20,30,4010, 20, 30, 40 cents on the first four days. How many cents will it hold on day 55?

Example 10

medium
Maya saves 1010 cents each day. After day 11 she has 1010 cents. How many cents does she have after day 66?

Example 11

hard
A pattern starts at 33 and adds 22 each step: 3,5,7,9,…3, 5, 7, 9, \ldots. What is the 77th number?

Example 12

easy
A growing pattern uses dots: figure 11 has 11 dot, figure 22 has 33 dots, figure 33 has 55 dots, figure 44 has 77 dots. How many dots does figure 55 have?

Example 13

easy
A growing staircase has 2,4,6,82, 4, 6, 8 blocks in the first four steps. How many blocks does step 77 have?

Example 14

hard
A train of tiles grows like this: figure 11 uses 44 tiles, figure 22 uses 77 tiles, figure 33 uses 1010 tiles, figure 44 uses 1313 tiles. How many tiles will figure 88 use?

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, ___, ___.

Example 3

easy
A pattern goes red, blue, red, blue, red, ___. What color is next?

Example 4

easy
What is the repeating core of: circle, square, square, circle, square, square?

Example 5

easy
Continue the number pattern: 2, 4, 6, 8, ___.

Example 6

easy
A pattern is clap, stomp, clap, stomp. What kind of pattern is this?

Example 7

easy
What comes next: triangle, triangle, circle, triangle, triangle, ___?

Example 8

easy
Fill the blank: 5, 10, 15, ___, 25.

Example 9

easy
A bead pattern is big, small, small, big, small, small. How many beads are in one repeat?

Example 10

easy
Which is an AB pattern: (a) X O X O, or (b) X X O X X O?

Example 11

medium
A pattern is A, B, B, A, B, B, A, B, B. What is the 8th item?

Example 12

medium
Continue: 1, 2, 4, 8, ___. What is the rule and next term?

Example 13

medium
A pattern repeats every 44 shapes: star, moon, sun, cloud. What is the 10th shape?

Example 14

medium
In the pattern 3,6,9,12,…3, 6, 9, 12, \ldots, what is the 6th term?

Example 15

medium
A color pattern is red, red, blue, red, red, blue. How many reds are there in the first 99 items?

Example 16

medium
Find the missing terms: 20, 18, 16, ___, ___, 10.

Example 17

medium
A pattern is square, circle, square, square, circle, square, square, circle, square. What pattern core repeats?

Example 18

challenge
A pattern repeats every 55 beads: red, red, blue, green, green. In the first 2323 beads, how many are green?

Example 19

challenge
A growing pattern uses 11 tile, then 33, then 55, then 77 tiles. How many tiles does the 6th figure use?

Example 20

challenge
Pattern A repeats every 22 (X, O) and pattern B repeats every 33 (1, 2, 3) side by side. At what position do X and 1 first line up again together after position 1?

Example 21

medium
A pattern is □,△,△,□,△,△\square, \triangle, \triangle, \square, \triangle, \triangle. What is the 7th shape?

Example 22

medium
Continue the shrinking pattern: 100, 90, 80, ___, ___.

Example 23

easy
Look at the pattern: red, blue, red, blue, red, ___. What color is next?

Example 24

easy
What comes next? circle, square, circle, square, ___.

Example 25

easy
Look at the beads: yellow, green, yellow, green, ___. What color is the next bead?

Example 26

easy
What comes next? cat, dog, cat, dog, cat, ___.

Example 27

medium
Look at the train: big, small, big, small, ___. What car is next?

Example 28

medium
What comes next? star, moon, star, moon, star, ___.

Example 29

hard
A pattern is: hop, jump, hop, jump, hop, jump, hop, ___. What is next?

Example 30

easy
Look at the pattern: red, red, blue, red, red, blue, ___. What color is next?

Example 31

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

Example 32

easy
What is the repeating core of: A, A, B, A, A, B, A, A, B?

Example 33

easy
What comes next? sun, sun, cloud, sun, sun, cloud, sun, ___.

Example 34

medium
Which is an AAB pattern: (a) X, O, X, O or (b) X, X, O, X, X, O?

Example 35

easy
Find the next two numbers: 2, 4, 6, 8, ___, ___.

Example 36

easy
Continue the pattern: 5, 10, 15, 20, ___.

Example 37

easy
What is the rule for this pattern: 20,30,40,5020, 30, 40, 50?

Example 38

medium
Find the missing numbers: 5, 10, ___, 20, ___, 30.

Example 39

easy
A row on a 100-chart shows 41, 42, 43, 44, ___, ___, 47, 48, 49, 50. Fill in the blanks.

Example 40

easy
A column on a 100-chart shows 7, 17, 27, ___, 47. Fill in the blank.

Example 41

easy
Extend the 100-chart row: 61, 62, 63, 64, 65, 66, ___, ___, ___, 70.

Example 42

medium
A 100-chart row is 81, 82, 83, ___, 85, 86, 87, ___, 89, 90. Fill in the blanks.

Example 43

medium
On a 100-chart, the column under 44 shows 4, 14, 24, 34, ___, 54, ___, 74. Fill in the blanks.
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Background Knowledge

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

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