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NUMBER SERIES

In Banking exams, number series plays a very important role in scoring. You might be weak in Mathematics, but this chapter would help you to cross the cut-off. But in Mains, questions from this part hardly come.

So students let's strive to score good marks in prelims and in mains exams too to be in the safe zone. Remember, a serious hardworking student practice all types of sum and leave no chapter untouched.

This chapter also falls under the GI section of SSC, Railway, UPSC, State PCS Exams, etc. After learning the chapter from here, you will be a masterpiece in Number Series, I bet!!

We will practice this chapter for the banking exams because this will nurture all concepts and easier to solve questions on this chapter in exams other than banking.

What do we mean by Number Series?

Actually, it is an array of numbers having a common difference or a common ratio in between.

E.g.: 1, 4, 7, 10, 13, 16, 19, ... and 2, 10, 50, 250, 1250, ...

In the above series, can we feel any common thing in between the numbers?

The former series tells us about the common difference of 3 and the latter tells us about the common ratio of 5.

Okay, let me tell you in detail –

> In the series 1, 4, 7, 10, 13, 16, 19, ... Subtract any number from the number which is following it.

Say, 4 is subtracted from 7.

Similarly, 7 is subtracted from 10, 10 is subtracted from 13, and goes on.

You will find a common answer that is 3. This is known as a common difference.

So this series is also said to be in Arithmetic Progression.

> In the series 2, 10, 50, 250, 1250,... Divide any number by its preceding number.

Say, 10 is divided by 2, 50 is divided by 10, and goes on.

You will find the answer is 5, common for all. This is a common ratio.

And this series is Geometric Progression.

Try these questions below –

1) 2, 3, 5, 8, 12, ?

2) 5, 10, 16, 23, 31, ?

3) 8, 11, 14, 17, 20, ?

4) 2, 6, 18, 54, ?

5) 1, 2, 6, 24, 120, ?

Hint - 1: Find the common difference or common ratio and then observe the numbers carefully.

Hint - 2: Check the increasing level. If it increases slowly, then go for finding common difference else common ratio is the only possible deciding factor.

Types of Number Series:

There are 3 types of Number series –

TYPE – I COMMON DIFFERENCE SERIES

Here, the common difference is the only solution to crack the series. The numbers in this series increase or decrease slowly.

Yes, we have to identify the series by checking the magnitude of the rate of increase or decrease.

The given examples below will help you to understand the key concept.

Examples:

1) 1, 3, 6, 10, 15, ?

In the above series, we can observe the rate of increase which is not high. If we find the common difference series by subtracting each number from its following number or if we add the rate to the previous number in the series, then we get this –

2) 1, 11, 26, 47, 75, ?

3) 1, 11, 24, 44, 77, ?

4) 1, 101, 188, 258, 309, ?

Here 13, 17, 19, 23 are prime numbers.

TYPE –II COMMON RATIO SERIES

Unlike the previous type, the magnitude of the rate of increase or decrease will be very high. That rate is also termed as a Multiplication factor.

It may be more than 1 or less than 1.

Let’s observe the below examples to know how do we identify common ratio series.

Examples:

1) 1, 2, 4, 16, 192, ?

The magnitude of the rate of increase is very high. And we cannot solve it by finding a common difference method. We have multiplied the multiplication factor by the previous number

2) 1, 3, 18, 216, 5184, ?

3) 2, 4, 12, 60, 420, ?

Here 2, 3, 5, 7, 11 are prime numbers.

4) 1, 0.25, 0.125, 0.25, 3, ?

TYPE –III MISCELLANEOUS SERIES

There are some series which we have to learn or get familiar with-

And there are many more. It would be easier for you to gain some time in the exam hall if you get familiar with the above series. Try to find more series of similar kinds. The below examples will make you understand how to solve these series.

Examples

1) 8, 27, 125, ?, 1331