Patterns in Maths - Definition, Types & Examples

Patterns in Maths are sequences of numbers, shapes or symbols that follow a specific rule or repeat in a certain way. They help us understand order and recognise relationships in different forms. Patterns can appear in counting, shapes or even letters. 

Keep reading to discover the different types of patterns and the specific rules they follow, with simple examples to help you understand how each pattern works in Maths.

What is a Pattern in Maths?

A pattern in mathematics is something that repeats or follows a rule. It can be numbers, shapes, letters, or objects that are arranged in a certain order. When we see a pattern, we can guess what will come next by looking at how it changes.

Patterns help us understand how things work. They show us how numbers grow, how shapes change, and how things are connected. We can find patterns in counting, adding, multiplication, and even in designs or nature.

For example, look at this number pattern: 

2, 4, 6, 8, 10...

Each number is going up by 2. That means the next number will be 12.

Now look at this shape pattern:

Triangle, Square, Pentagon... 

Each shape is adding one more side. A triangle has 3 sides, a square has 4, and a pentagon has 5. So the next shape would have 6 sides, i.e. a hexagon.

Rules for Patterns in Maths 

Every number pattern in maths follows a rule. This rule helps us figure out how the pattern works and what comes next. To understand a pattern, we need to look carefully at how each number changes from one step to the next.

There are two main directions a number pattern can follow. If the numbers are increasing, it is called an ascending pattern. If the numbers are decreasing, it is called a descending pattern.

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Ascending Patterns

An ascending pattern is when the numbers get bigger each time. This usually happens through addition or multiplication.

For example, in the sequence 5, 10, 15, 20, 25, we can see that each number is five more than the one before. That means the rule for this pattern is to add five every time.

Another example is 3, 6, 12, 24, 48. Here, each number is twice the previous one. So, the rule is to multiply by two each time.

Descending Patterns

A descending pattern is when the numbers get smaller each time. This often involves subtraction or division.

Take the pattern 50, 45, 40, 35, 30. Each number is five less than the one before. The rule here is to subtract five every time.

In the pattern 81, 27, 9, 3, each number is one-third of the previous one. The rule here is to divide by three at each step.

How to Find the Rule in Any Pattern?

To discover the rule, first check whether the numbers are increasing or decreasing. Then look at the change between each pair of numbers. Try using addition, subtraction, multiplication, or division to see what connects them.

Test your idea across the whole pattern. If it works for each step, then you have found the correct rule.

Example of a Pattern with a Special Rule

Look at the sequence 1, 4, 9, 16, 25. These numbers are not increasing by the same amount, but there is still a pattern.

Each number is the square of a whole number.

• One times one is one

• Two times two is four

• Three times three is nine

• Four times four is sixteen

• Five times five is twenty-five

This type of pattern follows a rule based on square numbers. It shows how patterns can go beyond simple addition or multiplication and still follow a regular rule.

Types of Patterns in Maths 

Let’s look at the different types of patterns in maths, along with examples to make them easy to understand.

1. Repeating Patterns

Repeating patterns are patterns where a certain group of elements appears over and over in the same order. These can be numbers, shapes, colours, or letters.

Example: Pink,  White, Blue,  Pink, White, Blue,...

This kind of pattern is commonly seen in designs like borders, wallpapers, and floor tiles. You can extend it simply by repeating the group again.

2. Growing Patterns

In a growing pattern, each step in the sequence increases in a regular way. The change can be in size, value, or number.

Example: 1, 2, 4, 8, 16...

Here, each number is doubled. This is a typical growing pattern and shows exponential growth.

Growing patterns are important in understanding multiplication and also show up in real-life situations like compound interest or population growth.

3. Shrinking Patterns

Shrinking patterns work in the opposite way to growing patterns. In these, each step becomes smaller by a regular rule.

Example:  100, 50, 25, 12.5...

In this case, each number is divided by 2. Shrinking patterns help us understand division and fractional reasoning. They are also seen in examples like depreciation of value or decreasing water levels.

4. Letter Patterns

These patterns use alphabets arranged in a meaningful sequence. They often follow alphabetical order or a set rule.

Example: A, C, E, G, I...

In this sequence, each letter skips the next one in the alphabet. Letter patterns are useful in puzzles, code-breaking, and language-based reasoning.

5. Shape Patterns

Shape patterns involve repeating or changing geometric shapes in a sequence. These patterns may involve rotation, reflection, or resizing of shapes.

Examples: Circle, Triangle, Square, Circle, Triangle, Square...

Recognising shape patterns helps in learning symmetry, geometry, and design structures.

4. Number Patterns

Number patterns are one of the most common types of patterns in maths. These are sequences of numbers that follow a mathematical rule.

Subtypes of Number Patterns:

Arithmetic Pattern: In this type, the same number is added or subtracted each time.

Example: 2, 5, 8, 11, 14...

The rule is "add 3." Arithmetic patterns are useful in budgeting, timelines, and schedules.

Geometric Sequence: A geometric sequence is a list of numbers where each number is found by multiplying the previous number by the same value each time. This value is called the common ratio.

Example:  3, 12, 48, 192...

Start with 3. Multiply by 4 each time 

• 3 × 4 = 12

• 12 × 4 = 4

• 48 × 4 = 192

So, the common ratio is 4.

Rule: To find any term in the sequence, use the formula:
an = a1 × rⁿ⁻¹

here:
a1 is the first number (here, 3)
r is the common ratio (here, 4)
n is the position in the sequence

Fibonacci Pattern: This is a special pattern where each number is the sum of the two before it.

Example: 0, 1, 1, 2, 3, 5, 8, 13...

It appears in nature, such as leaf arrangements and spiral shells.

Patterns in Maths Solved Example

Problem 1: Number Pattern

Sequence: 1, 4, 9, 16, ___

Solution:
Look at how the numbers are increasing:
1 = 1 × 1
4 = 2 × 2
9 = 3 × 3
16 = 4 × 4

This is a pattern of square numbers. The next term is 5 × 5 = 25

Problem 2: Geometric Number Pattern

Sequence: 5, 10, 20, 40, ___

Solution:
Each number is multiplied by 2.
5 × 2 = 10
10 × 2 = 20
20 × 2 = 40

So, the next number is 40 × 2 = 80

Problem 3: Shape Pattern

Pattern: Circle, Hexagon, Circle, Hexagon, ___

Solution:
This pattern repeats every two shapes: Circle, Hexagon.
The next shape after the second Hexagon is a Circle.

Problem 4: Letter Pattern

Pattern: M, O, R, V, ___

Solution:
Check the alphabet positions: 

M (13), O (15), R (18), V (22) 

The gaps are: +2, +3, +4

The next gap should be +5 

22 + 5 = 27, which is not in the alphabet, so start back from A (1) 

27 – 26 = 1 → A

So, the next letter is A

Problem 5: Mixed Number Pattern

Sequence: 1, 2, 6, 24, ___

Solution:

Each number is the product of the previous number and the next whole number:
1 × 1 = 1
1 × 2 = 2
2 × 3 = 6
6 × 4 = 24

Now: 24 × 5 = 120

This is a factorial pattern: n!

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