**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,**

1^{st} series: 1 2 3

2^{nd} series: 4 5 5

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

**Let us see:**

**Here,**

1^{st} series: 4 5 6 7 8 9

2^{nd} series: 9 8 7

3^{rd} 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.

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