Number Seriese

Category : 6th Class

                                                                                     Number Series

 

Learning Objectives

  • What is a Number Series
  • Types of Problems

 

What is a Number Series?

A number series is a sequence of numbers which follow a particular rule. Each element of a series is called a 'term'. In this chapter, we will analyse the pattern of different kind of number series that a particular series follow and find the missing term to continue the pattern.

 

Example

Find the missing term in the given series.

2, 8, 32, 128, __.

(a) 512                          (b) 510

(c) 516                          (d) 520

(e) None of these

 

Answer (a)

Explanation: Option (a) is correct. The relationship between the terms or the pattern that the given series follows is as below.

Therefore, the next term or missing term of the given series will be

 

Find the missing term in the following number series.

2, 3, 5, 7, 11, 13__.

(a) 15                            (b) 19

(c) 17                            (d) 14

(e) None of these

 

Answer (c)

Explanation: Option (c) is correct. The given number series is the sequence of consecutive prime number. So, the next number or the missing term will be 17,

 

Commonly Asked Questions

 

Find the next number.

64, 32, 16, 8, __

(a) 2                                          (b) 4

(c) 6                                           (d) 0

(e) None of these

           

            Answer (b)

Explanation: Option (b) is correct because in the given number series, each number is half of its previous number. So the required number or the missing term will be 4.

Rest of the options is incorrect because of the correctness of option (b).

 

What comes in place of question mark (?) in the series given below?

1, 4, 10, 19, ?

(a) 30                            (b) 31

(c) 32                            (d) 33

(e) None of these

 

Answer: (b)

Explanation: Option (b) is correct because the series goes as following-

So the required next term in the series will be

Rest of the options is incorrect because of the correctness of option (b)

 

A single number series can have more than one series.

            Example

Look at the following:

(i) 1  4  2  5  3  6

 

Clearly,

1st series:    1      2          3

2nd series:   4      5          5

(ii) 4 9 5 3 6 8 7 2 8 7 9 1

Let us see:

 

                       

Here,

1st series:   4 5 6 7 8 9

2nd series:   9 8 7

3rd series:   3 2 1

 

Commonly Asked Questions

 

Find the missing number in the following series

8 2 9 1 10 0…………..

(a) 12                            (b) 11

(c) 3                                (d) 5

(e) None of these

 

Answer (b)

Explanation: Option (b) is correct.

Let us see:

 

Rest of the options is incorrect because of the correctness of option (b).

 

What comes next in the following series?

9 4 8 6 7 8………..

(a) 6                                          (b) 9

(c) 5                                          (d) 4

(e) None of these

 

Answer (a)

Explanation: Option (a) is correct.

Let us see:

 

Rest of the options is incorrect because of the correctness of option (a).

 

A number series may have some arithmetical signs also.  

Example

Look at the following:

 

(1)

(2)

 

Commonly Asked Questions

 

What comes in place of the question mark (?)?

 

(a)                      (b)

(c)                      (d)

(e) None of these


Answer (b)

Explanation: Option (b) is correct because in the given series, 4 is multiplied by 1, 2, 3 and 4 respectively.

Rest of the options is incorrect because of the correctness of option (b),

 

What comes in place of the blank space?

 

(a)                      (b)

(c)                      (d)

(e) None of these

 

Answer (c)

Explanation: Option (c) is correct because in the given series, 3 is divided by 5, 6, 7 and 8, respectively.

Rest of the options is incorrect because of the correctness of option (c).

 

Types of Problems

Problems Based on Addition

Such series are based on addition of numbers.

 

Example 1

1, 2, 3, 4…….

Series pattern: 1 is added to every number to get the next number.

 

Example 2

3, 5, 7………….

Series pattern: 2 is added to every number to get the next number.

 

Commonly Asked Questions

 

Find the next number in the following series.

0, 2, 4, 6……..

(a) 8                                          (b) 3

(c) 5                                           (d) 7

(e) None of these

 

Answer (a)

Explanation: Option (a) is correct because the series goes as following:

Rest of the options is incorrect because of the correctness of option (a).

 

What will come in place of the blank space?

1, 10, 19____

(a) 28                                   (b) 29

(c) 30                                    (d) 31

(e) None of these

 

Answer (a)

Explanation: Option (a) is correct because the series goes as following:

 

Therefore, the required number will be

Rest of the options is incorrect because of the correctness of option (a).

 

Problems Based on Substraction

Such series are based on subtraction of numbers,

 

Example 1

4 3 2 1

Series pattern: 1 is subsaturated from every number to get the next number.

 

Example 2

7 5 3 1

Series pattern: 2 is subsaturated from every number to get the next number.

 

Commonly Asked Questions

 

Find the missing number in the series given below.

9 6 3 ______

(a) 8                                          (b) 2

(c) 7                                          (d) 0

(e) None of these

 

Answer: (d)

Explanation: Option (d) is correct because the series goes as following

 

Rest of the options is incorrect because of the correctness of option (d).

 

What comes next in the given series?

20, 19, 17, 14, 10,_____

(a) 4                              (b) 3

(c) 5                              (d) 1

(e) None of these

 

Answer (c)

            Option (c) is correct because the series goes as following:

 

     

Therefore, next number in the series will be

Rest of the options is incorrect because of the correctness of option (c).

 

Problems Based on Multiplication

Such series are based on multiplication of numbers.

 

Example 1

1 2 4 8

Series pattern: Each element is multiplied by 2 to get the next element.

Let us see:

           

        Example 2

Series pattern: Each element of the series is a multiplication of same numbers and the numbers taken for this multiplication are in forward or increasing order sequence.

 

Commonly Asked Questions

 

What comes next in the given series?

(a)                      (b)

(c)                      (d)

(e) None of these

 

Answer (c)

Explanation: Option (c) is correct because 3 is multiplied by 1, 2, 3, 4 and 5, respectively.

Rest of the options is incorrect because of the correctness of option (c).

 

Find the missing number.

2, 6, 8, 10, 12,

(a) 3                              (b) 1

(c) 4                              (d) 7

(e) None of these

 

Answer (c)

Explanation: Option (c) is correct because the series goes as following:

 

                 

Rest of the options is incorrect because of the correctness of option (c).

 

            Problems Based on Division

Such problems are based on division of numbers.

Example 1

Series pattern: 1 is divided by 1, 2, 3 and 4, respectively.

 

Example 2

 

Series pattern: 4 divides 2, 3 and 4, respectively.     

 

Commonly Asked Questions

 

Fill in the blank with suitable option

 

(a)                             (b)

(c)                             (d)

(e) None of these

 

Answer (b)

Explanation: Option (b) is correct because in the given series, 8 divides 5, 6, 7, 8 and 9, respectively. Hence,, after dividing 7, 8 will definitely divide 8,

Rest of the options is incorrect because of the correctness of option (b),

 

What comes next?

(a)                      (b)

(c)                      (d)

(e) None of these

 

Answer (a)

Explanation: Option (a) is correct because in the given series, '6' is divided by 2, 3, 4 and 5, respectively.

Rest of the options is incorrect because of the correctness of option (a),

 

Counting a Particular Number

In such problems, a candidate is said to count a particular number in the series as per a given condition. For example, in the series '1 2 4 3 2 4 5 2 4', you can be asked to count 4 coming just before 3.

 

Commonly Asked Questions

 

How many 2s come just after 3 in the given series?

5 1 3 4 2 3 2 4 8 4 3 2 2 2

(a) 5                                          (b) 2

(c) 4                                          (d) 1

(e) None of these


Answer (b)

Explanation: Option (b) is correct. Just see the reason below:

2s coming just after 3 are encircled.

Rest of the options is incorrect because of the correctness of option (b).

 

            How many 5s come just before 8 in the series given below?

8 5 7 8 5 8 5 5 8 5 8 8 7 5

(a) 4                                       (b) 5

(c) 1                                       (d) 3

(e) None of these

 

Answer: (d)

Explanation: Option (d) is correct. Just see the reason below:

 

5s coming just before 8 are encircled.

Rest of the options is incorrect because of the correctness of option (d),

 

            Miscellaneous Problems

Such problems do not have any fixed pattern like addition, substraction, multiplication, division and number counting. Such series come before you as a surprise.

 

Example 1

21,   12,      30,    03,

Series pattern: The addition of both digits of every number is 3. Let us see:

 

 

Example 2

11, 21, 31, 81.

Series pattern: The last digit of every number is 1.

 

Commonly Asked Questions

 

Find the missing number in the series given below.

15, 25, 5,__,05, 65.

(a) 2                                            (b) 5

(c) 4                                            (d) 3

(e) None of these

 

Answer (b)

Explanation: Option (b) incorrect because the last digit in every number is 5.

Rest of the options is incorrect because of the correctness of option (b).

 

What can be fit in the blank space?

10, 16, 11…….18.

(a) 20                                      (b) 25

(c) 21                                      (d) 15

(e) None of these

 

Answer (d)

Explanation: Option (d) is correct because each number in the given series starts with 1. Rest of the options is incorrect because of the correctness of option (d).

 

Commonly Asked Questions                    

 

Find the missing number.

15, 20, 30, 50, __.

(a) 100                                      (b) 80

(c) 70                                         (d) 90

(e) None of these

 

Answer (d)

Explanation: Option (d) is correct because the series has following pattern:

 

Therefore, missing number will be

Rest of the options is incorrect because of the correctness of option (d).

 

Fill the blank circle.

 

(a) 14                                        (b) 23

(c) 21                                        (d) 13

(e) None of these

 

Answer (d)

Explanation: Option (d) is correct because digits sum of every number is 4. Let us se

 

Rest of the options is incorrect because of the correctness of option (d).

 

            What comes next in the series given in the box?

79, 87,_, 89, 83, 91.

(a) 82                            (b) 81

(c) 48                            (d) 62

(e) None of these

 

Answer (b)

Option (b) is correct because the series pattern goes as following;

 

           

Rest of the options is incorrect because of the correctness of option (b).

 

            See the following series carefully and fill the blank space, 

(a)                      (b)

(c)                      (d)

(e) None of these

 

 

Answer: (b)

Explanation: Option (b) is correct because in the given series, 4 is divided by 6 7 8 and 9, respectively. Hence, after division by 8, number 4 will definitely be divided by 9.

Rest of the options is incorrect because of the correctness of option (b).

Fill in the blanks in the given series.

1, 1, …….. 3, 5, 5, 8, …… 2, 2.

(a) 3, 8                          (b) 4, 3

(c) 3, 4                          (d) 5, 3

(e) None of these

 

Answer (a)

Explanation: Option (a) is correct because in the given series/ the numbers are in pairs and the series will be written as following.

 

Rest of the options is incorrect because of the correctness of option (a).

 

Summary

  • A number series is a sequence of digits or numbers or both.
  • A number series may have some mathematical signs like ‘+’ (plus) ‘-‘ (minus) ‘x’ (multiplication) and ‘’ (division).                         
  • A number series may be in increasing or decreasing order.
  • Same number/numbers can be repeated in a number series.
  • Number series are based on addition, substraction, multiplication and division.
  • A number series may follow miscellaneous patterns.

Other Topics

Notes - Number Seriese
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