Number Patterns: Types and Rules

Number Patterns, in math, are finding out specific relationships between sets of numbers or different shapes. Mathematicians or scientists look for patterns in numbers to derive solutions. 

There are different types of patterns in mathematics:

• Numerical patterns
• Image patterns
• Word patterns
• Logic patterns

Among these, Number patterns are quite often detected in mathematics. Number patterns are an arrangement or series of numbers based on certain logic or relationship between numbers. Number patterns are mainly categorized into Geometric patterns and Arithmetic/Algebraic patterns.

Key Terms: Number Patterns, Geometric Patterns, Algebra, Series, Odd Numbers, Even Numbers

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What are Number Patterns?

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The repetitive order of numbers in certain specific patterns or rules is called number patterns. To recognize patterns, the identification of the relationship between numbers in the series is important to note.

• Even number patterns are numbers that range from 2, 4, 6, 8, 10. It can be divided by two.
• Similarly, odd number patterns are numbers ranging from 3,6,9, 12 and more. It can be divided by three.

Some examples of numerical patterns include:

• Even numbers pattern -: 2, 4, 6, 8, 10, 1, 14, 16, 18, …
• Odd numbers pattern -: 3, 5, 7, 9, 11, 13, 15, 17, 19, …
• Fibonacci numbers pattern -: 1, 1, 2, 3, 5, 8 ,13, 21, … and so on.

Example of Patterns

Also Check:

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Arithmetic Number Patterns

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Arithmetic (also known as algebraic patterns) are patterns which are placed in rules of addition or subtraction of numbers.

• Here, the numbers in the series are increasingly/decreasingly adding or increasingly/decreasingly subtracting by a unique number.
• The numbers in the series are consecutively added or subtracted by a specific number.
• The goal is to find the specific number and crack the pattern.

For example, let’s assume a consecutive increase or decrease of the number in the given series. The numbers here are consecutively increasing by 50.

⇒ 50, 100, 150, 200, 250, 300….

The numbers here are consecutively decreasing by 2.

⇒ 24, 22, 20, 18, 16, 14, 12 …

Two-Stage Type Arithmetic Pattern

In a Two-stage type arithmetic pattern, the difference in consecutive numbers in a series are in an arithmetic pattern.

Example: What is the pattern in 1, 3, 6, 10, and 15…?

Ans: Thus, 3 - 1 = 2, 

6 - 3 = 3,

10 - 6 = 4,

15 - 10 = 5, and so on.

Hence, we get an arithmetic pattern 2, 3, 4, 5…

And now if we add 6 to the last number in the given series, the next number in the series would be 15 + 6 = 21.

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Geometric Number Patterns

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Geometric patterns, in math, are patterns which are placed in rules of multiplications or division of numbers.

• Numbers in the series are increasingly/decreasingly multiplied or increasingly/decreasingly divided by a unique number.
• The numbers in the series are consecutively multiplied or divided by a specific number.
• For Example-consecutive multiplication or division of numbers in a pattern by a unique number.

The numbers here are consecutively multiplied by 6.

⇒ 18, 24, 32, 26, 42 … 

The numbers here are consecutively divided by 9

⇒ 81, 72, 54, 45, 36 …

Also Check:

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Rules for Patterns

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The basic foundation of number patterns is that the numbers are placed or arranged according to some rule. To crack the rule, the first step is to identify the type of series.

Increasing number series

If the numbers in the series show an increase in the numbers, these patterns usually contain addition or multiplication rules.

Decreasing number series

If the numbers in the series show a decrease in the numbers, these patterns usually contain subtraction or division rules.

Finding Missing Terms

Assume a pattern as 1, 4, 9, 16, 25, __. Here, every number is the square of its position number. Thus, the missing terms occur in n = 6. Thus, in case the missing term is x_n, then xn = n². Thus, if n = 6, then x_n = (6)² = 36.

Difference Rule

Here, consider 1, 5, 9, 13,__. In this pattern, the difference between two pairs of the sequence should be found. Following this, the remaining elements of the pattern can be determined. Thus, the difference between the terms is 4, which is, if 4 and 1 are added, we can obtain 5, while if we add 4 and 5, we get 9 and so on.

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Fibonacci Pattern

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The Fibonacci pattern is a series of numbers in which each number in the series is the addition of the two numbers before it.

Examples of Fibonacci Sequence in Nature: 0, 1, 1, 2, 3, 5, 8, 13, …

• Third number in the series (1) = First number (0) + Second number (1)
• Fourth number in the series (2) = Second number (1) +Third number (1)
• Fifth number in the series (3) = Second number (1) +Third number (2) and so on.

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Repeating Pattern

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In a number series, if the number patterns are in repeating order, then it is called a Repeating pattern.

For Example: 1, 2, 3, 4, 1, 2, 3, 4, ...

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Types of Number Patterns

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Some of the types of patterns, in math, are:

• Growing Pattern: If the numbers in patterns are in increasing order, then the number pattern is called the Growing pattern. The numbers are consecutively increasing by specific numbers. For example: 4, 8, 12, 16, 20…
• Shirking Pattern: If the numbers in the pattern are in decreasing order, then the number pattern is called a Shrinking pattern. The numbers are consecutively decreasing by a specific number. For example: 25, 20, 15, 10, 5…
• Repeating Pattern: In the case of a Repeating Pattern, the rule keeps repeating over and over.

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Things to Remember

• Patterns can be found when determining specific relationships between sets of numbers or different shapes.
• There are three types of number patterns, namely Growing Patterns, Shrinking Patterns, and Repeating Patterns.
• The Fibonacci pattern can be defined as a series of numbers wherein each number in the series is the addition of the two numbers before it.
• The repetitive order of numbers in specific patterns or rules is called number patterns.