Number series is defined as a series in which a sequence or a pattern is given, you need to find the logical pattern and answer the questions accordingly. Series is one of most crucial topic for banking exams because five questions are asked in Pre and main exam of Banks i.e. SBI PO, SBI Clerk, IBPS PO, IBPS Clerk, RBI Assistant etc.

Short Tricks to analyse number series:-

- If the series is rapidly increasing or decreasing it should be Multiplication or Division Series.
- If the series is slowly increasing or decreasing it should be Addition or Subtraction Series.
- Remember in exam five question are asked in which three questions are easy means as soon as you see it you are able to detect the pattern and two are difficult, so don’t waste time on those two series questions.
- Remember Square roots up to 1 to 30 and cube roots up to 1to 20.
- Questions are of two types in some types a series is given and you have to find the next or missing number in the series. In another type of questions a series is given and you have to find the wrong number in the series.

To understand the concept of series following types of series should be kept in minds i.e.

- Constant difference series.

- Addition Series.
- Subtraction Series.
- Division Series.
- Multiplication Series.

- Odd or Even Number Series.
- Prime Number Series
- Squares or Cubes series.
- Alternate Pattern Series.
- Fibonacci Series.
- Arithmetic Series.
- Geometric Series.
- Triangular series.
- Mixed Pattern Series.

- Wrong number series.

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**Constant difference series.**

**Addition Series**: – In addition series, a specific numbers, prime numbers, odd numbers and even numbers are added to get the next number in the series, based on some pattern.

**Example**:-

2, 4, 6, 8, 10, ?

**Explanation:-**

We see in the above series next number is obtained by adding 2

2+ 2 = 4

4+ 2= 6

6+2 = 8

8+2 =10

10 + 2=12

Thus, the number in Place of? Should be 12

**Subtractions Series: –**In subtraction series, specific numbers, prime numbers, odd numbers, and even numbers are subtracted to get the next number in the series, based on some pattern.

** **** Example:****–**

20, 17, 14, 11, 8, ?

**Explanation:-**

We see in the above series next number is obtained by subtracting 3

20 – 3 =17

17 – 3 = 14

14 – 3 = 11

11 – 3 = 8

8 – 3 = 5

Thus, the number in Place of ? Should be 5.** **

**Multiplication Series:**– In multiplication series, specific number or decimal number is multiplied to obtain the next number in series.

**Example:-**

**4, 20, 100, 500, ?**** **

**Explanation:-**

We can see in the above series next number is obtained by multiplying each term by 5

4 × 5 = 20

20 × 5= 100

100 × 5=500

500 × 5= 2500

Thus, the number in Place of ? Should be 2500

**Division Series: –**In division series, Specific number or prime number/odd number/even number is divide to obtain the next number in series.

** ****Example:**

**4096, 1024, 256, ? 16, 4**** **

**Explanation:-**

We can see in the above series next number is obtained by dividing each term by 4.

4096 ÷ 4 = 1024

1024 ÷ 4 =256

256 ÷ 4 = 64

64 ÷ 4 =16

16 ÷ 4 = 4

Thus, the number in Place of ? Should be 64.

**Consecutive Odd / Even Number Series.**

In series based on odd and even number followed by its consecutive odd or even number and one number is missing in it.

**Example:-**

**3, 5, 7,?, 11, 13**

** ****4, 6, 8, 10, 12,?**

**Explanation:-**

**3, 5, 7, ? , 11, 13**

5 is consecutive odd number of 3, 7 is consecutive odd number of 5 and so on, the required consecutive number of 7 is 9. Thus the required number is 9.

**4, 6, 8, 10, 12 , ?**

6 is consecutive even number of 4, 8 is consecutive even number of 6 and so on, the required consecutive number of 12 is 14. Thus the required number is 14.

**Prime number Series.**

As we Know that prime numbers are the numbers which is divisible by itself and one. This series is based on a prime number followed by its next prime, and one number is missing in it.

**Example:-**

**3, 5, 7, 11, ?, 19 ,23 **

**Explanation:-**

This series is based on prime number starting from 3. So the required prime number come in the place of ? is 13.

**Square / Cube series.**

**Square series:-**

In this type of series, each numbers in series is a perfect square following a particular pattern in a specific order.

**Example:-**

**121, 144, 169,196, 225, ?**

**Explanation:-**

In the above series we can see that the series is increasing and also the difference between the first and second number is maximum. So it is perfect square of particular numbers shown as follows:

11^{2 }= 121

12^{2 }=144

13^{2 }=169

14^{2 }=196

15^{2 }= 225

16^{2 }= 256

Thus, the number in Place of ? Should be 16^{2} i.e. 256

**Cube series:-**

In this type of series, each numbers in series is a perfect cube following a particular pattern in a specific order.

** Example:-**

** 64, 125, 216, 343, 512,?**

** Explanation:-**

In the above series we can see that the series is increasing and also the difference between the first and second number is maximum. So it is the perfect cube of particular numbers shown as follows:

4^{3 }= 64

5^{3 }= 125

6^{3 }= 216

7^{3 }= 343

8^{3 }= 512

9^{3 }= 729

Thus, the number in Place of ? Should be 9^{3} i.e.729

**Alternate Pattern Series.**

In this type of series, different numbers are used alternatively to form a sequence or series**.**

**Example:**

** 29, 4, 25, 6, 21, ? , 17, 10**

**Explanation:-**

As we see in this series number is increasing then decreasing so it follow an alternate pattern of subtracting 4 and adding 2 as shown below:

29 – 4 =25

4 + 2 = 6

25 – 4 = 21

6 + 2 = 8

21 – 4 = 17

8 + 2 = 10

Thus, the number in Place of ? Should be 8.

**Fibonacci Series.**

In this type of series, the number is obtained by addition or multiplication of two previous numbers belongs to the same series.

**Example:**

**2, 3, 5, 8, 13, 2l, 34, ?**

**Explanation:-**

In the above series we can see that the third number is obtained by adding first and second number shown as follows:

2 + 3 = 5

3 + 5= 8

5 + 8 = 13

8 + 13 = 21

13 + 21 = 34

21 + 34 =55

Thus, the number in Place of ? Should be 55.

**Arithmetic Series:-**

In this type of series the difference between a term and its preceding or previous term is constant in the entire series, it is represented by formula.

**T _{n} = a + (n – 1) × d**

Where, T_{n} is n^{th} term, a is First term, n is number of terms, d is difference between second term and first term.

**Example:**

10, 16, 22, 28, 34,?

**Explanation:-**

By using formula

a = 10, n = 6, d = 16 – 10 = 6

= 10 + (6 – 1) × 6

= 10 + 5×6

= 10 + 30

= 40

Thus, the number in Place of ? Should be 40.

**Geometric series:-**

In this type of series the ratio between a term and its preceding or previous term is constant in the entire series, it is represented by formula.

** T _{n = }a r ^{n-1}**

Where, T_{n} is n^{th} term, a is First term, n is number of terms, r is common ratio in which second term is divided by first term.

**Example:**

32, 16, 8, 4, 2, ?

**Explanation:-**

By using formula

**T _{n = }a× r ^{n-1}**

a = 32, n = 6, r = 16 ÷ 32 = ½

= 32 × (½)^{6-1 }

= 32 × 1/32

=1

Thus, the number in Place of ? Should be 1.

**Triangular pattern series.**

In this type of series, difference between the numbers is not constant but difference between their differences or next two terms is constant.

**Example:-**

36, 43, 53, 66, 82,?

**Explanation:-**

In the above series the difference between the first term and second term, second term and third term is not constant, but the difference between their differences is constant.

Thus, the number in Place of ? Should be 101.

**Mixed Pattern Series.**

In this type of series, different operators such as addition, Subtraction, squares, cubes etc. are applied to find the next number in the series.

**Example:-**

**5, 7, 21, 55, 117, ?**

**Explanation:-**

In this series the pattern is n^{2} – 2, where n is the square of even numbers.

5 + 2^{2} – 2 = 5 + 4 – 2 = 7

7 + 4^{2} – 2 = 7 + 16 – 2 = 21

21+ 6^{2} – 2 = 21 + 36 – 2 = 55

55 + 8^{2} – 2 = 55 + 64 – 2 = 117

117 +10 ^{2} – 2 = 117 +100–2 = 215

Thus, the number in Place of ? Should be 215.

**Example:-**

30, 41, 54, 69, ?

**Explanation:-**

In the above series the pattern is n^{2 }+ 5

5^{2 }+ 5 = 25 + 5 = 30

6^{2} + 5 = 36 + 5 = 41

7^{2} + 5 = 49 + 5 = 54

8^{2} + 5 = 64 + 5= 69

9^{2 }+5 = 81 + 5 = 86

Thus, the number in Place of ? Should be 86.

- In mixed series there is a pattern in which number is addition and square of itself, then, gain added to the number to obtain the next number in series.

**Example:-**

144, 225, 306,?, 711

** Explanation:-**

144 + (1+4+4)^{2 }= 144 + 9^{2 }= 144+81 = 225

225 + (2+2+5) ^{2} = 225 + 9^{2} = 225 + 81 = 306

306 + (3+0+6)^{2} = 306 + 9^{2 }= 306 + 81= 387

387 + (3+8+7) ^{2} =387 +18^{2 }=387 +324 = 711

Thus, the number in Place of ? Should be 387.

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**Wrong number series.**

In this type of series, all the numbers follows a pattern expect one, you have to find that wrong number as your answer or replace the wrong number from the alternative given in question, in order to make series correct.

**Example:-**

64, 81, 99, 121,144

** **

** Explanation:-**

In the above example all numbers are square, expect 99.

8^{2 }= 64

9^{2} = 81

10^{2} = 100

11^{2} = 121

12^{2}= 144

Therefore the wrong number in the series is 99, it is replaced by 100.

2) **Example:-**

5, 7, 10, 14, 22, 33

**Explanation:-**

5 + 2 = 7

7 + 3 = 10

10 + 5 = 15

15 + 7 = 22

22 + 11 =33

In the above series prime numbers are added to get the next number, where 14 is the wrong number, it is replaced by 15.

**Thanks.**

## Author : Prasad, Namrata | Sevenmentor Pvt Ltd

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