The number patterns are essentially a series of the numbers in the specified sequence that helps in establishing a common relationship between the pattern and the numbers. The whole numbers in Maths are natural numbers alongside zero. These numbers include all the positive integers alongside zero. The numbers pattern is not restricted to any specific type. There are several patterns of whole numbers including sequences of even, odd, descending, ascending, cube numbers, square numbers, and multiples of any of the numbers.
Understanding the Number Pattern
The numbers tend to be very interesting since they have a series of sequences and beautiful patterns that are fascinating. The pattern of numbers can be described as the list of numbers that has the common feature. When you solve problems related to specific number patterns in Mathematics, it helps in improving Mathematical reasoning and logical thinking capabilities. For solving any question that is related to whole number patterns in the sequence, the rule that is used for creating the pattern needs to be understood first.
Number Patterns Using Dots in Maths
The number patterns are also represented in Maths using the dots. The whole numbers were first represented using dots that were arranged in numerous elementary shapes of square, line, triangle, and rectangle amongst others. The 4 basic shapes that are used for representing numbers in the form of dots include: Line, Rectangle, Triangle, and Square. It is possible to represent every whole number in the form of the line using dots.
Line
Rectangle
Square
Triangle
Every whole number can be represented in the form of a line with the help of dots.
Example:
1 is represented as •
2 is represented as • •
3 is represented as • • •
4 is represented as • • • •
Any number which can be represented using a rectangle is known as a rectangular number. Generally, it is possible to represent all even numbers as the rectangular numbers. Representing numbers as equilateral triangles with the help of dots is known as triangular representation and numbers that can be represented as equilateral triangles are known as triangular numbers. It is possible to represent the ideal square whole numbers using dots.
The representation of a few rectangular numbers is shown in the table below.
Number | Rectangular Representation | Number | Rectangular Representation |
6 | • • • • • • | 10 | • • • • • • • • • • |
8 | • • • • • • • • | 12 | • • • • • • • • • • • • |
Representing the numbers in the form of an equilateral triangle using dots is called the triangular representation and the numbers which can be represented in the form of equilateral triangles are called the triangular numbers.A few triangular numbers are represented in the figure below:
The perfect square whole numbers can be represented in the shape of squares with the help of dots. The representation of a few square numbers are shown in the table below.
Number | Rectangular Representation | Number | Rectangular Representation |
4 | • • • • | 16 | • • • • • • • • • • • • • • • • |
9 | • • • • • • • • • | 25 | • • • • • • • • • • • • • • • • • • • • • • • • • |
Types of Patterns in Maths:
There are different patterns of numbers in Mathematics. Some of the varying pattern types for numbers in Maths are as follows. Even numbers, Odd numbers, Square numbers, Cube numbers, Geometric sequence, Arithmetic sequence, and Fibonnaci numbers.
Odd Numbers: Set of all numbers which are not divisible by two completely
Even Numbers: Set of all numbers which are divisible by 2 completely
Square Numbers: Sequence of numbers which are perfect squares of whole numbers
Cube Numbers: Pattern of numbers consisting of perfect cubes of whole numbers
Fibonacci Numbers: A sequence of numbers in which the next term is equal to the sum of the two preceding terms
Arithmetic Sequence: Sequence of numbers with a common difference
Geometric Sequence: Sequence of numbers with a common ratio
Number Patterns Examples:
1. Find the missing number in the sequence 2, 3, 6, 7, 4, 28, 5, _ , 15
Solution:
To find the missing number in the sequence, what is a number pattern used should be understood.
In this sequence, every third term is the product of two preceding terms.
i.e. 2 x 3 = 6
7 x 4 = 28
5 x _ = 15
So, the missing number in the sequence is 3
2. Find the missing number in one of the types of patterns in Maths shown below.
5, 7, 12, 14, 19, _, 26
Solution:
In the above sequence,
T2 = T1 + 2
T3 = T2 + 5
T4 = T3 + 2
T5 = T4 + 5 and so on.
So, the 6th term can be obtained as:
T6 = T5 + 2 = 19 + 2 = 21
So, the missing term in the sequence is 21.
