Number Patterns Whole Numbers

Patterns of Whole Numbers:

Number patterns are the series of numbers in a specified sequence which generally establishes the common relationship between the numbers in the pattern. Whole numbers in Mathematics are the natural numbers along with zero. These numbers include all the positive integers along with zero. Number patterns are not restricted to a specific type. There are infinite patterns of whole numbers which include a sequence of odd, even, ascending, descending, multiples of any number, square number, cube numbers etc.

What is a Number Pattern?

Numbers are highly fascinating and amazing because they have a number of beautiful patterns and sequences that are truly interesting. A pattern of numbers is a list of numbers which has a common feature. Solving problems related to number patterns in Maths improves the logical thinking and Mathematical reasoning capabilities of the learner. To solve any question related to patterns of whole numbers in a sequence, the rule used to create the pattern is to be initially understood.

Number Patterns in Maths Using Dots:

Whole numbers were initially represented with the help of dots arranged in a few elementary shapes like line, square, rectangle and triangle etc. The four basic shapes used to represent the numbers in the form dots are:

1. Line

2. Rectangle

3. Square

4. 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 that can be represented in the form of a rectangle is called a rectangular number. In general, all even numbers can be represented as rectangular numbers. 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 Math:

A few important types of patterns in Math include the following:

• 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

1. Find the missing number in one of the types of patterns in Math 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.

Fun Quiz:

1. Which of the following numbers can be expressed as a square using dots?

1. 9

2. 7

3. 3

1. Which of the following numbers cannot be represented as triangles using dots?

1. 6

2. 10

3. 4

1. What are Different Types of Numbers in Mathematics?

The basic elements of Mathematics are numbers. There are a wide range of numbers used in Mathematical computations which include:

• Natural Numbers: All counting numbers

• Whole numbers: Natural numbers including zero

• Prime numbers: Numbers which has only one and itself as the factors

• Composite numbers: Numbers which can be expressed as a product of prime factors

• Odd numbers: Numbers which are not completely divisible by 2

• Even numbers: Numbers which are completely divisible by 2

• Square numbers: Numbers which are the products of whole numbers multiplied by itself

• Integers: Odd and even numbers along with zero

• Decimals and fractions: Numbers that can be expressed in the form of decimal points or as ratios.

• Rational numbers: All numbers that can be expressed in the form of a fraction in which denominator is not equal to zero.

• Irrational numbers: Numbers which cannot be represented in the form of a fraction with non zero denominator

• Real numbers: All rational and irrational numbers

• Imaginary numbers: Numbers which are assumed to be existing just to explain few Mathematical concepts

2. What is Arithmetic and Geometric Sequence in Context of What is a Number Pattern?

Arithmetic sequence is a sequence of numbers in which there is a common difference between the terms. i.e. The difference between any two consecutive terms remains constant throughout the sequence.

Example: Multiples of any whole number. The common difference here is that number whose multiples are written in a sequence.

A geometric sequence is a pattern of numbers in which there exists a common ratio between the consecutive terms. i.e. The ratio of any two consecutive terms remains the same throughout the sequence.

Example: 2, 6, 18, 54, 162 … (The common ratio here is 3)