Patterns

We know that Mathematics is all about numbers. It basically involves the study of different patterns. There are different types of patterns in Mathematics, such as image patterns, logic patterns, number patterns, word patterns etc. The most common patterns in Mathematics are number patterns. These patterns are quite familiar to the students who study Mathematics frequently. Especially, they are everywhere in Mathematics. So, let’s discuss the definition of pattern.

In simple words, Number patterns are all predictions. Let’s discuss a few examples of numerical patterns are:

1. Pattern of even numbers -: 2, 4, 6, 8, 10, 1, 14, 16, 18, 20…

2. Pattern of Odd numbers -: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21….

3. Pattern of Fibonacci numbers  -: 1, 1, 2, 3, 5, 8 ,13,  … and so on

We are going to discuss the definition of pattern in Mathematics with a few solved example problems. In this article, we are going to focus on various patterns and pattern definition in maths.

Pattern Definition-

• A pattern can be defined as a series or sequence that generally repeats. We observe patterns – things like colors, actions, shapes, or other sequences that repeat – everywhere in our daily life.

• Math patterns are basically sequences that repeat according to a rule or rules. In math, a rule can be defined as a set way to calculate or solve a problem.

In Mathematics, the patterns can be related to any type of event or object. If the set of numbers are related to each other in any specific kind of rule, then the rule or manner is known as a pattern. Sometimes, patterns can also be known as a sequence. They are finite or infinite in numbers.

For example, in the given sequence 2,4,6,8,? Each number is increasing by the number 2. So, the last number will be 8 + 2 which is equal to 10.

According to the definition of pattern there is a common type of math pattern known as the number pattern. Number patterns can be defined as a sequence of numbers that are ordered based upon a rule. Now, according to the pattern definition there are many ways to figure out the rule, such as:

• Use a number line to see the distance or the difference between the numbers or what the numbers have in common.

• Look at the last one or two digits or the first digit of the numbers to see if they repeat in any special manner.

• Look at the numbers and see if there is any pattern, like taking each number and multiplying by 2 for instance.

• Think about the common number patterns, like counting by 2s, 5s, or 10s.

• You can also find the difference between the numbers

It’s important to remember that a number pattern can have more than one solution and a combination of rules present. In this case, try to think of the simplest rule that is possible, like adding 2 or multiplying by 3 with a difference of 4.

There are Various Different Types of Number Patterns:

• The Arithmetic Pattern

•  The Geometric Pattern

• The Fibonacci Pattern

Let’s Discuss the Rules for Patterns in Maths-

Now to construct a pattern, we have to know about some of the rules. To know about the rule for any type of pattern, we need to understand the nature of the sequence and the difference between the two successive terms in the pattern.

Finding the Missing Term: If we consider a pattern like 1, 4, 9, 16, 25,?. In this pattern, it is clear that every number is the square of their position number that is position 1 gives 1 square, second position gives two square that is equal to four. The missing term takes place at n = 6. So, if the missing term is xn, then we can write that xn = n2. Here, the value of n = 6, then xn = (6)2 which is equal to 36.

The Difference Rule: Sometimes, it is easy and simple to find the difference between two successive terms in a pattern. For example, consider 1, 5, 9, 13,… In this type of pattern, first, we need to find the difference between the two pairs of the sequence. After that, we need to find the remaining elements of the pattern. In the given problem, the difference between the terms is equal to 4, that is if we add 4 and 1, then we get 5, and if we add 4 and 5, then we get 9 and so on.

Different Types of Patterns in Mathematics –

In Discrete Mathematics, we have these 3 types of patterns:

• Repeating Patterns– If the number pattern changes in the same value every time, then the pattern can be known as a repeating pattern. Example: 1, 2, 3, 4, 5 ,6…

• Growing Patterns – If the numbers are present in an increasing form, then the pattern can be known as a growing pattern. Example 34, 40, 46, 52, 56 …..

• Shirking Patterns – In the shirking pattern, the numbers are generally  in decreasing form. Example: 42, 40, 38, 36, 32..

Questions to be Solved-

Example 1) Determine the Value of  Variables A and B in the Following Pattern.

85, 79, 73, 67, 61, 55, 49, 43, A, 31, 25, B.

Solution) We have been given  the sequence:85, 79, 73, 67, 61, 55, 49, 43, A, 31, 25, B.

Here, the number here is decreasing by 6

The previous number of A is 43. So, A will be 43 – 6, P = 37

The previous number of B is 25. So, B will be 25 – 6, Q = 19

Therefore, the value of A is 37 and B is 19.

Q1. What are Number Patterns in Mathematics and What are the Four Rules of Maths? What are the Common Types of Patterns?

Ans. Number pattern can be defined as a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers present among them. For example: 0, 5, 10, 15, 20, 25, 30 (differs by a value of 5)

The Four Basic Mathematical operations are -addition, subtraction, multiplication, and division. These four operations have application even in the most advanced mathematical theories.

The common types of patterns are –

1. Single piece pattern

2. Split piece pattern

3. Loose piece pattern

4. Gated pattern

5. Match pattern

6. Skeleton pattern