The Patterns of Whole Numbers
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.
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.
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.
Fun Quiz:
1. Which of the following numbers can be expressed as a square using dots?
a. 9
b. 7
c. 3
2. Which of the following numbers cannot be represented as triangles using dots?
a. 6
b. 10
c. 4
FAQs on Number Patterns Whole Numbers
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 the 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)
3. What are the various number types in Mathematics?
The basic Maths element is the numbers. There are a wide array of numbers that are utilised in Maths computations. These types of numbers are Whole numbers, Natural numbers, Prime numbers, composite numbers, Even numbers, Odd numbers, Integers, Square numbers, Fractions or decimals, Rational numbers, Irrational numbers, Real numbers, and Imaginary numbers. Each of these number types has its own definition that governs their calculations and operation in Maths.
4. What is the meaning of an arithmetic sequence with an example?
The arithmetic sequence is essentially the sequence of numbers where you can find common difference between terms. This means the difference between any of the two consecutive terms will remain constant throughout the specific sequence. The example or instance of the arithmetic sequence includes multiples of any of the whole numbers. The common difference is the specific number whose multiples are noted or written in the sequence.
5. What is the meaning of the geometric sequence with an example?
The geometric sequence is essentially the sequence or pattern of numbers where there is a common ratio between consecutive terms. This means the ratio of any of the two consecutive terms will remain the same throughout the entire sequence. The example of the geometric sequence can be denoted as follows: 2, 6, 18, 54, 162….and so on. The common ratio that stands out here is 3.
6. Are Vedantu notes on “Number patterns whole numbers” reliable?
Yes, the Vedantu notes on “Number patterns whole numbers” are very reliable. These notes are prepared by well qualified and highly knowledgeable experts with considerable experience in the subject. These notes are well prepared with lucid explanations, detailed interpretation, and excellent illustrations wherever required. The comprehensive coverage of the topic and exceptional presentation helps the students to grasp the concept in its entirety which is hugely beneficial in the exams.
7. How can I access the Vedantu notes on “Number patterns whole numbers”?
If you want to refer to the “Number patterns whole numbers” notes from Vedantu then you can download these notes on your device. These notes are available in the form of PDF file and they can be downloaded from either the Vedantu app or the website. Once you are on the relevant section or page, you can click on the “Download PDF” option and the notes will be downloaded for free on your device for offline usage.
