Patterns
The study of mathematics includes numbers and the different patterns in which they are listed. There are different types of patterns in mathematics, such as number patterns, image patterns, logic patterns, word patterns, and so on. The number pattern is the most commonly used one since students are aware of even numbers, odd numbers, skip counting, etc., which help in understanding these patterns easily.
Definition of Patterns
Patterns include a series or sequence that generally repeats itself. The patterns that we observe in our daily lives are those of colors, actions, shapes, numbers, etc. They can be related to any event or object and can be finite or infinite. In mathematics, patterns are a set of numbers arranged in a sequence such that they are related to each other in a specific rule. These rules define a way to calculate or solve problems. For example, in a sequence of 3,6,9,12,_, each number is increasing by 3. So, according to the pattern, the last number will be 12 + 3 = 15.
The following figure shows the different types of patterns and sequences that can be formed with numbers.
Number Pattern
Number pattern is the most common type of pattern in mathematics where a list of numbers follows a certain sequence based on a rule. The different types of number patterns are algebraic or arithmetic patterns, geometric patterns, and the Fibonacci pattern.
Arithmetic Pattern
Arithmetic Pattern, also known as the algebraic pattern, is a sequence of numbers based on addition or subtraction to form a sequence of numbers that are related to each other. If two or more numbers in the sequence are given, we can use addition or subtraction to find the arithmetic pattern. We can also determine the missing number in a given sequence by using addition or subtraction.
For example, let us find the missing numbers in the series: 4, 8, ___, 16, 20, ___ .
In the above pattern, we can see that each number increases by 4. Hence, the rule which is followed for this pattern is that we add 4 to the previous term to get the next term. We can find the missing numbers using this pattern. Therefore, the missing numbers are 8 + 4 = 12 and 20 + 4 = 24.
Geometric Pattern
Geometric pattern is a sequence of numbers that are based on multiplication and division. If two or more numbers in the sequence are provided, we can easily find the unknown numbers in the pattern using multiplication and division operations. For example: 6, 18, 54, __, 486, __
In the given series, it can be seen that each number is obtained by multiplying 3 with the previous number. So, the missing number numbers can also be determined using this rule. Therefore, the missing numbers are 54 × 3 = 162 and 486 × 3 = 1458.
Fibonacci Pattern
The Fibonacci Pattern is a sequence of numbers in which each number in the sequence is obtained by adding the two previous numbers together. The sequence starts with 0 and 1. Observe this Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, and so on. Here, we can see the pattern that is followed is: 0 + 1 = 1, 1 + 1 = 2 , 1 + 2 = 3 , 2 + 3 = 5, 3 + 5 = 8.
Rules for Patterns
To create a complete pattern, there are a set of rules to be considered. To apply the rule, we need to understand the nature of the sequence and the difference between the two successive numbers. It takes some amount of guess work and checking to see whether the rule works throughout the whole series.
There are two basic divisions to find out the rules in number patterns:
 When the numbers in the given pattern get larger, they are said to be in an ascending order. These patterns usually involve addition or multiplication.
 When the numbers in the given pattern get smaller, they are said to be in a descending order. These patterns usually involve subtraction or division.
Let us understand this with an example:
Example: Find the pattern rule for the series: 81, 27, 9.
 The first observation is that it is a descending pattern.
 So, let us start with the smallest number 9. What could be done to 9 to get 27? We see that 9 × 3 = 27.
 Now, let us see if this pattern works for the next number. 27 × 3 = 81.
 Observing this, if we understand the series in the given order, we get to know that the pattern rule that is followed here is: "Divide by 3".
 This means if we divide 81 by 3, we get 27, then when we divide 27 by 3 we get 9.
Similarly, we can find out the pattern rules for any given series of numbers.
Types of Patterns
There are three types of patterns that are commonly used in mathematics:
 Repeating Pattern  A pattern that keeps repeating over and over again in the sequence of numbers is called the repeating pattern.
 Growing Pattern  If the numbers or objects are arranged in an increasing order in a sequence, that pattern is called a growing pattern.
 Shirking Pattern  A shirking pattern is a pattern where numbers or objects are arranged in a decreasing order.
Observe the following figure which shows a repeating pattern of the shapes.
Related Topics
Important Points:
Here are some of the key points to be remembered when dealing with patterns.
 Number patterns are not restricted to a few types. They could be ascending, descending, multiples of a certain number, or series of even numbers, odd numbers, etc.
 Learning patterns enhances our capability to observe patterns. Observing a pattern pushes us to think and identify the rule which can continue the pattern.
 Patterns can be of shapes, objects, and colors as well and not just numbers.
 In an arithmetic sequence, each successive term is obtained by adding the common difference to its preceding term.
 In a geometric sequence, each successive term is obtained by multiplying the common ratio to its preceding term.
Solved Examples

Example 1: Determine the value of D in the sequence of numbers: 11, 17, 23, 29, D, 41, 47, 53
Solution: In the given sequence, we can see the pattern of every number is increasing by adding the number 6 to obtain the next consecutive number.
11 + 6 = 17, 17 + 6 = 23, and so on.
Hence, the missing number D is 29 + 6 = 35.

Example 2: Determine the value of P in the sequence of numbers: 1, 4, 9, P, 25
Solution: In the given sequence, the pattern that we see is that every number is the square of the counting numbers.
The square of 1 is 1, the square of 2 is 4, and so on.
Hence, the missing number 'P' is a square of 4 which is 16.
FAQs on Patterns
What is Meant by Patterns in Maths?
In Math, a pattern is also known as a sequence. The list of numbers that are arranged using specific rules is called a pattern. For example, in the series: 2,4,6,8,10.... , the numbers are arranged in a pattern which shows even numbers.
Mention Two Different Types of Number Patterns.
The two different types of number patterns are:
 Arithmetic Pattern  This is a sequence of numbers which are related to each other and are usually based on addition or subtraction.
 Geometric Pattern  This is a sequence of numbers that are related to each other and are based on the multiplication and division operation.
What is a Number Pattern?
A number pattern shows the relationship between a given set of numbers. It is defined as the list of numbers that follow a certain pattern or sequence. For example, in the given series: 5, 10, 15, 20, 25, 30... , we can see that each term in the pattern is obtained by adding 5 to the previous term.
How to Teach Patterns in Math?
Patterns can be taught through simple exercises like arranging different beads in a string in a particular order, or taking the building blocks of different shapes and sizes and arranging them in a particular sequence which creates a series. For number patterns, the factors, multiples, squares, and cubes of numbers help in understanding patterns easily
What are the Common Types of Patterns?
The common types of patterns are:
 Number patterns
 Arithmetic patterns
 Geometric patterns
 Fibonacci patterns
Identify the Type of Pattern for the Sequence 4, 6, 8, 10, 12.
The pattern 4, 6, 8, 10, 12 shows an arithmetic pattern or an arithmetic sequence, as each term in the pattern is obtained by adding 2 to the previous term.
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