Number series is an important topic and requires a lot of practice because the series can follow any logic hence it is very important that you do rigorous practice of this topic to ace this. This topic comes in both prelims and mains examination and carries a lot of weightage in the examination. In prelims this topic carries 5 questions for 5 marks and in mains also you can get these questions for 4 marks. Considering the importance of this topic we will be covering it in this article. Make sure you read it well and understand the concept.
What is Number Series?
Number series basically refers to a topic in which there are certain numbers align in a series and follow a certain logic and either get increase or decrease subsequently. For example 2, 4, 6, 8, 10.
Things You Must Know Before Starting This Topic
Given below is the list of things that you must remember by heart to ace this topic:
 Learn tables upto 25
 Learn Squares upto 25
 Learn Cubes upto 25
 Learn Fractcions upto 25
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Types Of Number Series
1. Addition and Subtraction Series.
In this type of series the series is either increasing by adding a common number in it or it is decreasing by subtracting a common number in it.
For example: 4, 8, 12, 16, 20
the difference of two successive numbers is 4 hence you can understand that 4 is added in each number.
Similarly for Subtraction:
36, 30, 24, 18, 12. In this series the difference between the two numbers is 6 and hence you can understanding that the pattern followed in this number series is the subtraction of 6 in each subsequent number.
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2. Multiplication and Division Series
In multiplication series, the numbers are increasing but in a more rapid way for ex: 5, 25, 125, 625 so, here you can see that the series is increasing rapidly and if you will see then each increasing number is getting multiplied by 5 to get the next number. This is the approach you use to solve these types of question.
*One of the best way to know the number which is getting multiplied is to divide the highest number with second highest number of the series.
Same procedure is followed by Division series. The only difference is that the series gets decrease subsequently.
3. Square and Cube Series.
In these type of questions, your preacquired knowledge of cube and square will come handy and will be useful. For example 8 27 125 512 1331 2197
As you can see that 2^{3}=8, 3^{3}=27, 5^{3}=125,
then the next number which will follow the series is cube of 7 which is 343.
4. Mix Pattern Series.
In this type of series, the pattern is increasing in a mixed way which means that some number is getting multiplied along with the addition of a number. For example 5, 6, 13, 40, the pattern followed in this series is as given below:
Pattern: 5×1+1=6
6×2+1=13
13×3+1=40
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Number Series Question and Answer
Let’s Understand this topic better with Example:
Directions (110) : In each of these questions a number series is given. In each series only one number series is given. In each series only one number is wrong. Find out the wrong number.
Q1. 1 3 10 36 152 760 4632
(a) 3
(b) 36
(c) 4632
(d) 760
(e) 152
S1. Ans.(d)
Sol. The number should be 770 in place of 760 because X1+2, x2+2, x3+3 and so on
Q2. 12, 12, 18, 45, 180, 1170, ?
(a) 12285
(b) 10530
(c) 11700
(d) 12870
(e) 9945
S2. Ans.(a)
Sol. The pattern is
×1.0, ×1.5, ×(1 + 1.5), ×(1.5 + 2.5), ×(2.5 + 4), ×(4 + 6.5)
∴ ? = 10.5 × 1170
? = 12285
Q3. 67, 1091, 835, 899, 883, ?
(a) 889
(b) 887
(c) 883
(d) 894
(e) 896
S3. Ans(b)
Sol. Pattern of series –
67 + 4^{5} = 1091
1091 – 4^{4 }= 835
835 + 4^{3} = 899
899 – 4^{2} = 883
? = 883 + 4^{1} = 887
Q. In each of the following questions a number series is given. After the series a number is given followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the number given, following the sequence of the original series and answer the questions that follow the series.
Q6. 12, 30, 120, 460, 1368, 2730
16 (a) (b) (c) (d) (e)
What will come in place of (d) ?
(a) 1384
(b) 2642
(c) 2808
(d) 1988
(e) None of these
S6. Ans. (c)
Sol. The given series is based on the following pattern:
30 = 12 × 6 – 7 × 6
120 = 30 × 5 – 6 × 5
460 = 120 × 4 – 5 × 4
1368 = 460 × 3 – 4 × 3
2730 = 1368 × 2 – 3 × 2
Similarly,
(a) = 16 × 6 – 7 × 6 = 96 – 42 = 54
(b) = 54 × 5 – 6 × 5 = 240
(c) = 240 × 4 – 5 × 4 = 940
(d) = 940 × 3 – 4 × 3 = 2808
Hence, 2808 will come in place of (d).
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