Number Series: Concepts, Solved Examples, & Preparation Strategies

Number Series refers to the sequence or pattern of numbers following some sequence or pattern. Candidates need to find the missing or wrong number in the series.

In this article, we are going to cover the key concepts of Number Series along with the various types of questions, and tips and tricks. We have also added a few solved examples, which candidates will find beneficial in their exam preparation. Read the article thoroughly to clear all the doubts regarding the same.

What is a Number?

Before starting out the article on Number Series we must know what a Number is.

Numbers are the set of certain symbols of figures called digits, They are the building block of mathematics. They are used to count, measure, lebel, order and code objects. Decimal system is a commonly used number system in which we use digits and place value to write numbers. The combination of these digits representing a number is known as numeral. We read these numbers either by using Indian Number system or International Number System.

If you’ve learned Number System, you can move on to learning Partnership concepts here!

Indian Number System 

In Indian Number System, a comma divides every two digits to the left of the last three digits of a number.

According to Indian Number System, 2,13,47,83,696 will be read as “two arab thirteen crore forty seven lakh eighty three thousand six hundred ninety six”

International Number System 

In the International Number System, a common division divides every three digits to the left of the last three digits of a number. We read the numbers by following the table given below.

According to the Internal Number System, 2,134,783,696 will be read as “two billion one hundred thirty four million seven hundred eighty three thousand six hundred ninety six”.

Important Definitions 

Let us know some of the important definitions related to the number series.

Real Numbers 

The numbers that are not imaginary are called real numbers. They include natural numbers, whole numbers, rational numbers, irrational numbers and fractions.

Irrational Numbers 

The real numbers that cannot be expressed in the form of p/q are called irrational numbers. They include non terminating and non recurring decimal numbers.

Rational Numbers 

The real numbers which can be expressed in the form of p/q are called rational numbers. They include fractions, integers, decimals, natural numbers and whole numbers.

Natural Numbers

The numbers used for counting purposes are called natural numbers. They are also known as counting numbers.

Whole Numbers

The counting numbers with zero are known as whole numbers. The smallest whole number is 1.

Integers 

Whole numbers with negative natural numbers are known as integers. The positive natural numbers are called positive integers and negative numbers are called negative integers.

Fractions 

Fractions are numbers used to represent a part of a whole. The fraction has two parts such as numerator and denominator. It is written in the form of a/b, where a and b are integers and a is called numerator and b is called denominator.

Even Numbers

Numbers completely divisible by 2 are known as even numbers. Even numbers can be written as 2k, where k is an integer.

Odd Numbers

Numbers that are not completely divisible by 2 are known as odd numbers. These are the opposite of even numbers.

Prime Numbers

Prime Numbers are the numbers greater than 1 and they have only two factors, 1 and the number itself. 2 is the smallest and only even prime number.

When you’ve finished with Number Series, you can learn about Percentages concepts in depth here!

Types of Question Asked in Number Series 

Various types of questions are asked from the number series, Some of them are as follows.

1. Addition Series 

In this type of number series, specific numbers based on some pattern are added to get the next number.

2. Subtraction Series 

In this type of number series, specific numbers based on some pattern are subtracted to get the next number.

3. Multiplication Series 

In this type of number series, a particular type of number pattern is multiplied to get the next number.

4. Division Series 

In this type of number series, a particular type of number pattern is divided to get the next number.

5. Square Series 

In this type of number series, each number is a perfect square of a particular number pattern.

6. Cube Series 

In this type of number series, each number is a perfect cube of a particular number pattern.

7. Fibonacci Series 

In this type of number series, the next number is the addition of two previous numbers.

8. Alternating Series 

In this type of number series, multiple number patterns are used alternatively to form a series.

9. Mixed Operator Series 

In this type of number series, multiple operators are applied to get the next number in the series.

10. Arranging Number 

In this type of number series, candidates need to rearrange numbers, as specified, and then answer the given questions.

Also check Pipe and Cistern concepts here once you are through with Number series concepts!

How to Solve Question Based on Number Series – Know all Tips and Tricks 

Candidates can find different tips and tricks from below for solving the questions related to number series.

Candidates can find various tips and tricks from below for solving the questions related to the Number Series.

Tip # 1:  Candidates need to find the process involved in the given series such as addition, subtraction, multiplication, division, and so on to find out the correct answer.

Tip # 2: For arranging type series, candidates need to rearrange the given series by using various processes to find out the correct answer.

Tip # 3: We can write every prime number greater than 3 as (6k + 1) or (6k – 1), where k is a natural number.

Number Series Solved Sample Questions

Question 1: What should come in place of the question mark ‘?’ in the following series?

8, 15, ?, 50, 78, 113

Solution: The series follows the following pattern: 8 + 7 = 15

15 + 14 = 29

29 + 21 = 50

50 + 28 = 78

78 + 35 = 113

∴ The required term will be 29.

Question 2: What should come in place of the question mark ‘?’ in the following series?

76, 80, 71, 87, ?, 98

Solution: The series follows the following pattern: 76 + 22 = 80

80 – 32 = 71

71 + 42 = 87

87 – 52 = 62

62 + 62 = 98

∴ The required term in the series will be 62.

Question 3: What should come in place of the question mark ‘?’ in the following series?

23, 535, 486, 702, 677, 741, ?

Solution: The series follows the following pattern: 23 + (8)3 = 535

535 – (7)2 = 486

486 + (6)3 = 702

702 – (5)2 = 677

677 + (4)3 = 741

741 – (3)2 = 732

∴ The next term in the series will be 732.

Question 4: What should come in place of the question mark ‘?’ in the following number series?

45, 139, 561, 2811, 16873, ?

Solution: The series follows the following pattern: 45 × 3 + 4 = 139

139 × 4 + 5 = 561

561 × 5 + 6 = 2811

2811 × 6 + 7 = 16873

16873 × 7 + 8 = 118119

∴ The next term in the series will be 118119

Question 5: What should come in place of the question mark ‘?’ in the following series?

16, 40, 140, 630, 3465, ?

Solution: The series follows the following pattern: 16 × 2.5 = 40

40 × 3.5 = 140

140 × 4.5 = 630

630 × 5.5 = 3465

3465 × 6.5 = 22522.5

∴ The next term in the series will be 22522.5

Question 6: What should come in place of the question mark ‘?’ in the following number series?

72, 108, 216, 540, ?

Solution: The pattern of the above series is as follows, 72 × 1 = 72

72 × 1.5 = 108

108 × 2 = 216

216 × 2.5 = 540

540 × 3 = 1620

∴ The next term in the series will be 1620

Question 7: What should come in place of the question mark ‘?’ in the following number series?

1680, 210, 30, 5, ?, 0.25

Solution: 1680/8 = 210 210/7 = 30

30/6 = 5

5/5 = 1

1/4 = 0.25

∴ The next term in the series will be 1

Question 8: Select the option that will correctly fill in the blank and complete the following series.

37, 41, 43, 47, 53, 59, ?

Solution: Given series is a series of consecutive prime numbers starting from 39. The prime number immediately after 59 is 61.

Hence, 61 will complete the series.

Question 9: Find the wrong number in the given series.

37, 43, 55, 73, 99, 127

Solution: The series follows the following pattern: 37 + 6 = 43

43 + 12 = 55

55 + 18 = 73

73 + 24 = 97

97 + 30 = 127

∴ The wrong term in the given series is 99.

Question 10: Find the wrong number in the given series.

33, 133, 400, 800, 802, 1

Solution: The series follows the following pattern: 33 × 4 + 1 = 133

133 × 3 + 1 = 400

400 × 2 + 1 = 801

801 × 1 + 1 = 802

800 × 0 + 1 = 1

∴ The wrong term in the given series is 800

Exams where Number Series is Part of Syllabus

Questions come up often in various prestigious government exams some of them are as follows

• SBI PO, SBI Clerk, IBPS PO, IBPS Clerk
• SSC CGL, SSC CHSL, SSC MTS
• LIC AAO, LIC ADO
• RRB NTPC, RRB ALP
• UPSC
• MPSC
• KPSC
• BPSC
• WBPSC
• Other State Level Recruitment Examinations

We hope you found this article regarding Number Series was informative and helpful, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.

Number Series FAQs

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