Patterns in Mathematics

Introduction to Patterns

The study of mathematics includes numbers and the different patterns in which they are listed. There are different 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 helps in understanding these patterns easily. In this article, we will learn about number patterns, fill in the missing numbers and ask some questions based on them.

Patterns example

Definition of Patterns

Patterns include a series or sequence that generally repeats itself. The patterns we observe in our daily lives are those of colours, actions, shapes, numbers, etc. They can be related to any event or object and are finite or infinite. In mathematics, patterns are numbers arranged in a sequence 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.

Numbers Patterns in Math

A number pattern is the most common type in mathematics, where a list of numbers follows a certain sequence based on a rule. The types of number patterns are algebraic or arithmetic patterns, geometric patterns, and the Fibonacci pattern.

For example, let us find the missing numbers in the series: 4, 8, ___, 16, 20, ___ .

Ans: In the above pattern, we can see that each number increases by 4. Hence, the rule followed for this pattern is adding 4 to the last 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.

Rules for Patterns

To create a complete pattern, a set of rules must be considered. To apply the rule, we need to understand the nature of the sequence and the difference between the two consecutive numbers. It takes some guesswork and checking to see whether the rule works throughout the whole series.

There are two basic divisions to finding out the rules in number patterns:

• When the numbers in the given pattern get larger, they are said to be in ascending order. These patterns usually involve addition or multiplication.

• When the numbers in the given pattern get smaller, they are said to be in descending order. These patterns usually involve subtraction or division.

Solved Examples

Find the missing numbers.

Q1. 1, 2, 3, 4, 5, 6, ____, ____, ____, ____.

Ans: 7, 8, 9, 10.

Pattern rule: Add one to each number to find the next number.

6 + 1 = 7

7 + 1 = 8

8 + 1 = 9

9 + 1 = 10

Q2. 4, 7, 10, 13, 16, ____, ____, ____, ____.

Ans: 19, 22, 25, 28.

Pattern rule: Add 3 to each number to find the next number.

16 + 3 = 19

19 + 3 = 22

22 + 3 = 25

25 + 3 = 28

Q3. 27, 25, 23, 21, 19, ____, ____, ____, ____.

Ans: 17, 15, 13, 11.

Pattern rule: Subtract 2 from each number to find the next number.

19 - 2 = 17

17 - 2 = 15

15 - 2 = 13

13 - 2 = 11

Q4. 1050, 1060, 1070, 1080, ____, ____, ____, ____.

Ans: 1090, 2000, 2010, 2020.

Pattern rule: Add 10 to each number to get the next number.

1080 + 10 = 1090

1090 + 10 = 2000

2000 + 10 = 2010

2010 + 10 = 2020.

Q5. 31, 28, 25, 22, ____, ____, ____, ____.

Ans: 19, 16, 13, 10.

Pattern rule: Subtract 3 from each number to get the next number.

22 - 3 = 19

19 - 3 = 16

16 - 3 = 13

13 - 3 = 10.

Practice Questions

Q 1. Fill in the missing numbers.

1. 101 __ 103

Ans: 102

2. 104 __ 106

Ans: 105

3. 107 __ 109

Ans: 106

4. 110 __ 112

Ans: 111

5. 113 __ 115

Ans: 114

Q 2. Identify the number pattern and fill in the missing numbers.

1. 113, 122, 131, 140, ____, ____, ____, ____.

Ans: 149, 158, 167, 176.

2. 890, 880, 870, 860, ____, ____, ____, ____.

Ans: 850, 840, 830, 820.

3. 7, 14, 21, 28, ____, ____, ____, ____.

Ans: 35, 42, 49, 56.

4. 5, 10, 15, 20, ____, ____, ____, ____.

Ans: 25, 30, 35, 40.

5. 127, 125, 123, 121, ____, ____, ____, ____.

Ans: 119, 117, 115, 113.

Summary

First of all, we have seen the pattern. Then moving further, I learned about the number pattern. i.e. It 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 ). There are different ways to find the missing numbers in a pattern. In the end, we have seen some solved examples and practice problems to have a better command of the topic.