Competitive exams are becoming the major segment of our youths' life who are graduated and ambitious to get the well-settled career. It's definitely a tough task to get success in these examinations, but it becomes easier if you are aware of the important topics and the preparation strategies.

Competitive exams such as __ SSC__,

Number Series is the most important topic of Mathematics. In the number series questions, the series are based on sequences of numbers that follow a logical pattern based on basic arithmetic concepts and we have to detect that concept then predict the next number in the sequence by following the same logic. Only practice can help you to make it perfect.

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There are three types of questions which are generally asked from the number series.

** Type 1 - **There is a number series in which a certain number is missing. You need to find out the missing number.

**Ex -** 10, 22, 46, 94, 190,**?**

** Type 2 -** There is a numerical series in which a number is incorrectly placed. Basically, you are asked to detect the wrong number.

**Ex –** 4, 9, 16, 24, 36

** Type 3 -** A complete series of numbers is followed by an incomplete series of numbers. The incomplete number series must be solved in the same pattern as the complete number series.

There are various tricks to solve the number series problems provided by Mathematics. Check these tricks below –

If all the numbers are prime, even or odd.

If all the numbers have a particular divisibility.

If all the numbers are perfect squares or cubes.

If all the numbers succeed by a certain number of additions or subtractions or multiplications or divisions, or by adding their cubes and squares.

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As we talked about number series problems, some specific rules are applied logically in the number series.

A series can be created in many ways. In recognizing the pattern followed in the number series, an understanding of these different ways can help us. So, here we go with some types of standard series.

There are different methods to solve number series problems such as predicting the next number i.e. which number will come next by applying rules such as adding, subtracting, etc. or applying various tricks for shortcuts.

A series based on Perfect Squares is mostly based in a specific order of the perfect squares of numbers, and in this type of series one of the numbers is generally missing which you have to find.

The formula is used to solve the number series problems is Xn= n^{2}.

**Example –**

There is a number series. Get the next one:

441, 484, 529, 576, ?

(A) 565

(B) 484

(C) 625

(D) 615

**Ans –** 21^{2 }= 441

22^{2} = 484

23^{2} = 529

24^{2} = 576

25^{2} = 625

So, the answer is (C).

In this type, the series consists of the cubes of numbers which are in same order and you have to find out the missing or odd cube number.

The formula is used to solve the number series questions is Xn= n^{3}.

**Example –** 729, 6859, 24389, ?, 117649, 205379

(A) 52335

(B) 58937

(C) 59319

(D) 55324

**Ans –** 9^{3} = 729

19^{3} = 6859

29^{3} = 24389

49^{3} = 117649

59^{3} = 205379

In this example each cube number is added with 10 to become the next cube number. So, the missing one is **39 ^{3} = 59319 (C)**.

These are the numbers that can be written as a fraction or quotient in which both numerator and denominator are integers.

**Example –** Find out the smallest part, if 75 is divided into four parts proportional to 3, 5, 8, 9.

(A) 9

(B) 10

(C) 11

(D) 12

**Ans -** Ration = 3:5:8:9

Sum of ratio terms = 25

The smallest part is (75 x 3/25) = 9.

It is a mathematical sequence there is a fixed difference between the numbers. The next terms are obtained either by adding a fixed number or by subtracting it.

The formula used to solve the number series problems is Xn = x1 + (n – 1)d

**Example -** There is a number series. Get the next number:

2, 4, 6, 8, ?

(A) 9

(B) 10

(C) 11

(D) 12

**Ans –** The common difference between numbers is 2

So, the answer is (B) = 10.

It is a sequence in which each term of series is obtained by a fixed number multiplying or dividing the preceding number.

**Example –** 3, 9, 27, 81, ? Get the next number:

**Ans –** In this series each term is multiple of 3. So, the next one is 243.

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As the name suggests - a peculiar combination of Arithmetic and Geometric series forms the Arithmetico –Geometric series. An important property of this series is that in the Geometric Sequence there are differences of consecutive terms.

**Example -** 4, 18, 60, 186, ?

**Ans – **It follows the number series trick -

4, (4+2)x3, (18+2)x3, (60+2)x3

So the next one is (186+2)x3 = 564

It is the reverse of Arithmetico –Geometric series. In this series, the suggestive terms differences are in the Arithmetic Series.

**Example – **2, 7, 17, ?, 77 get the missing one.

**Ans –** It follows the number series trick -

2, (2x2)+3, (7x2)+3

So, the answer is (17x2)+3 = 37

Here we have catered the complete details regarding the Number Series and includes all the methods which are used in solving the number series problems.

We hope that the blog helped you to clear all your doubts like How to solve number series questions and which type of number series questions asked in the exams.

Still, if you have any query related to Number Series, feel free to ask in the below comment box.

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