# Number Series for competitive exams

What is a Series?

A series is a collection of numerical or verbal values/data which are separated by a comma and follows a certain pattern. There are various kind of series that follows various kind of patterns.

When we talk about number series, patterns include increasing value, decreasing value, square of value, cube of value and many other such patterns. You are supposed to find the next value in the series or find the missing term or other logical questions of that manner.

Number Series, along with other types of series has been an integral part of every competitive exam. In this chapter, we will discuss Number Series, along with its various types. We’ll also explain some examples of Number Series.

Study material for competitive exams

Also note that, What you learn in this chapter would be useful to you in every aptitude based competitive exam like SSC, IBPS, CMAT, CSAT etc.

Best of luck for the study.

## Pattern 1.

Increase in numerical value

Find the next term in the examples 1 to 10.

(Ex 1). 2, 4, 8, 14, 22,__

(A) 30 (B) 32 (C) 38 (D) 42

Solution :

When you analyze the above series, you can see that increase is +2, +4, +6, +8 and so on. The pattern is “increase of 2 in the difference” and so we can find further terms in this series by adding +10, +12 and like that.

2, 4, 8, 14, 22, 32
+2 +4 +6 +8 +10

That is (B).

(Ex 2). 8,11,14,17,20,__

(A) 25 (B) 26 (C) 30 (D) 23

Solution :

The pattern is very simple here +3, +3, +3 and so on.

therefore, the next term would be 20+3 = 23.

That is (D).

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(Ex 3). 4,16,36,64,100,__

(A) 120 (B) 144 (C) 200 (D) 150

Solution :

On observation, you can see that the pattern is ${ 2 }^{ 2 },{ 4 }^{ 2 },{ 6 }^{ 2 },{ 8 }^{ 2 },{ 10 }^{ 2 }$ and so on.

Therefore, the next term would be ${ 12 }^{ 2 }$ = 144

That is (B).

(Ex 4). 21,29,33,41,45,53,__

(A) 120 (B) 144 (C) 200 (D) 150

Solution :

On observation, you can see that the pattern is +8,+4,+8,+4,+8 and so on.

Therefore, the next term would be 53+4=57

That is (C).

(Ex 5). 4,4,8,24,96,__

(A) 192 (B) 480 (C) 288 (D) 960

Solution :

You can see that the pattern here is x 1, x 2, x 3, x 4 and so on.

Therefore, the next term would be 96 x 5 = 480.

That is (B).

## Pattern 2.

Decrease in numerical value

(Ex 6). 400, 200, 100, 50,__

(A) 30 (B) 25 (C) 40 (D) 35

Solution :

When you analyze the above series, you can see that the pattern to get the next term is $\div 2,\div 2,\div 2$ and so on.

Therefore, the next term is 50/2=25.

That is (B).

(Ex 7). 240,80,20,4__

(A) 1 (B) 2 (C) 2/3 (D) 1/3

Solution :

The pattern here is $\div 3,\div 4,\div 5$ and so on.

therefore, the next term would be 4/6=2/3.

That is (C).

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(Ex 8). 52,48,46,42,40,36,__

(A) 32 (B) 34 (C) 30 (D) 28

Solution :

The pattern here is -4, -2, -4, -2, -4, -2 and so on.

therefore, the next term would be 36-2 = 34

That is (B).

(Ex 9). 64,49,36,25,16,__

(A) 9 (B) 8 (C) 4 (D) 12

Solution :

The pattern here is ${ 8 }^{ 2 },{ 7 }^{ 2 },{ 6 }^{ 2 },{ 5 }^{ 2 },{ 4 }^{ 2 }$ and so on.

therefore, the next term would be ${ 3 }^{ 2 }$=9.

That is (A).

(Ex 10). 7/4,3/2,5/4,1,3/4,__

(A) 2/3 (B) 1/2 (C) 1/4 (D) 1/6

Solution :

In this kind of examples, it is hard to calculate the difference with normal analysis by eye and mind. We need to find the difference here. Let’s do this.

3/2 – 7/4 = -1/4 ( We’d deduct first term from the second to find the difference and so on )

5/4 – 3/2 = -1/4

1 – 5/4 = -1/4

So, there’s a difference of -1/4 or a decrease of 1/4 as a pattern so we can find the next term by decreasing 1/4 from the last term.

therefore, the next term would be 3/4 – 1/4 = 2/4 = 1/2.

That is (B).

We have discussed some basic examples along with the concept of Number Series here. Hope you have understood them well. If you have any suggestion about this chapter or for improvement of delivery method, grace us with your valuable comments in comments section or send us an email on admin@sscjobsindia.com.

Have a great learning experience.

Thank you and best luck for success.

Includes all chapters of Verbal Reasoning and useful for every competitive exam