**Different types of questions covered in this chapter as follows**

**Number Series****Letter Series****Alpha-Numeric Series****Continuous Pattern Series**

The candidates are required to identify the pattern involved in the formation of series and accordingly find the missing term to complete the series. Also, there may be some questions where one of the terms in the series is incorrect and the candidate is required to find out that term of the series by identifying the pattern involved in the formation of series.

There is no set pattern and each question may follow a different pattern or sequential arrangement of letters or digits, which you have to detect using your common sense and reasoning ability.

**On the basis of various types of questions that are asked in competitive exams, we have classified series into several types as follows.**

**Number Series**

Number series is a logical sequence of more than one element made of arithmetical digits. Logical sequence means that each element or term in a number series is obtained according to a certain rule or pattern. These series can be formed by applying various methods/ patterns.

Let us see the following number series 2, 4, 6, 8, 10,……

When we see the above series, we notice that each element is 2 more than its previous element. Thus, we can say that each element of the above-mentioned series is obtained following a rule.

i.e., Previous element + 2= Next element

There are no set rules. In each case, you have to discover the pattern adopted. There can be the omission of letters/ digits in an order, there can also be alternative order, such as first one letter/ digit is skipped, then two, then three and so on.

In various competitive exams, the questions based on number series are asked in two different patterns. On this basis, we have classified number series into the following two types

**Inserting the Missing Number**

In such types of questions, series of numbers is given with one number/term missing from its place. The candidate is required to recognize the pattern involved in the formation of the series and find the missing number accordingly.

Various different patterns are involved in the formation of the series. Now, let us discuss some most common pattern to the previous element to obtain the next element.

**Same Number Addition Series**

In this type of series, the difference between two consecutive elements is the same i.e., each time the same digit/ number are added to the previous element to obtain the next element.

**Ex 1: What comes in place of question mark (?) in the series given below?**

4, 8, 12, 16, 20, ?

(a) 18

(b) 21

(c) 19

(d) 24

**Solution: (d)**

In the given series, the difference between two consecutive elements is same i.e., 4.

In this type of series, the number added to each term is in increasing order.

**Ex 2: What comes in place of question mark (?) in the following number series?**

2, 3, 5, 8, 12, 17, ?

(a) 23

(b) 19

(c) 18

(d) 25

**Solution: (a)**

In the given series, the difference between two consecutive numbers is in increasing order i.e., 1, 2,3,4,5 and 6 respectively.

**Same Number Subtraction Series**

In this type of series, each time the same/number is subtracted from the previous element to obtain the next element and thus in such series, the difference between the two consecutive elements is the same.

**Ex 3: Replace the question mark (?) in the following number series with a suitable option.**

48, 43, 38, 33, 28, ?

(a) 24

(b) 18

(c) 23

(d) 19

**Solution: (c)**

Here, the difference between two consecutive elements is the same i.e., 5.

**Increasing Order Subtraction Series**

In this type of series, the difference between two consecutive elements is in increasing order

**Ex 4: What comes in place of question mark (?) in the following number series?**

95, 94, 92, 89, 85, 80,?

(a) 74

(b) 69

(c) 75

(d) 77

**Solution: (a)**

Here, the difference between two consecutive elements is in increasing order.

**Same Number Multiplication Series**

In this series, the ratio between two consecutive elements is the same, i.e., in this case, every time the previous element is multiplied by the same digit/number to obtained the next element.

**Ex 5: What comes in place of question mark (?) in the following number series?**

4, 12, 36, 108, 324, ?

(a) 520

(b) 680

(c) 475

(d) 972

**Solution: (d)**

In the given series, the previous element is multiplied by 3 to obtain the next element and therefore the ratio between two consecutive element is same.

**Multiplication Series in Increasing Order**

In this type of series, the element is multiplied with numbers in increasing order to obtained the next element.

**Ex 6: Replace the question mark (?) in the following number series with a suitable option.**

3, 3, 4.5, 9, 22.5, ?

(a) 27.3

(b) 24

(c) 55

(d) 67.5

**Solution: (d)**

In the given series, the ratio between two consecutive elements is in increasing order and element are multiplied by the numbers in increasing order.

**Same Number Division Series**

In this type of series, each time the previous element is divided by the same digit/number to obtain the next element.

**Ex 7: What comes in place of question mark (?) in the following number series?**

336, 168, 84, 42, 21, ?

(a) 17

(b) 10.5

(c) 15

(d) 14.5

**Solution: (b)**

In the given series, the previous element is divided by 2 to get the next element.

**Division Series in Increasing Order**

In this type of series, the element is divided by numbers in increasing order to obtain the next element.

**Ex 8: What comes in place of question mark (?) in the following number series?**

7200, 3600, 1200, 300, 60, ?

(a) 10

(b) 25

(c) 15

(d) 20

**Solution: (a)**

In the given series, elements are divided by 2, 3, 4, 5 and 6 respectively to obtain the next elements.

**Same Number Multiplication and Same Number Addition series**

In this type of series, the next element is obtained by multiplying the previous number by a certain number A1 and by adding a certain number of A2 in this multiplication.

**Ex 9: Replace the question mark (?) in the following number series with a suitable option.**

5, 11, 23, 47, 95, ?

(a) 191

(b) 185

(c) 194

(d) 198

**Solution: (a)**

In the given series, following pattern is used.

Next number = (Previous number × 2+ 1).

**Same Number Multiplication and Addition in Increasing Order Series**

In this type series, each previous element is multiplied by the same number while numbers in increasing order are added respectively, in this multiplication to obtain the next element.

**Ex 10: Replace the question mark (?) in the given series with suitable option.**

5, 11, 24, 51, 106, ?

(a) 178 (b) 210 (c) 185 (d) 217

**Solution: (d)**

In the given series, following pattern is used.

**Increasing Order Multiplication and Same Number Addition Series**

In this type of series, each previous element is multiplied respectively by numbers in increasing order and then a certain number is added in such multiplication to obtain the next element.

**Ex 11: Replace the question mark (?) in the given series with a suitable option.**

3, 6, 15, 48, 195, ?

(a) 978

(b) 897

(c) 688

(d) 945

**Solution: (a)**

In the given series, each previous element is multiplied by 1, 2, 3, 4 and 5, respectively and then 3 is added in such multiplication to obtain the next element.

**Increasing Order Multiplication and Increasing Order Addition Series**

In this type of series, the previous element is multiplied respectively by numbers in increasing order and the numbers in increasing order are respectively added in such multiplication to obtain the next element.

**Ex 12: What comes in place of question mark (?) in the following numbers series?**

4, 5, 12, 39, 160, ?

(a) 225

(b) 695

(c) 805

(d) 790

**Solution: (c)**

In the given series, the following pattern is used

**Same Number Multiplication and Same Number Subtraction Series**

In this type of series, each previous element is multiplied by a certain number and then a certain number is subtracted from this multiplication to obtain each next element.

**Ex 13: Replace the question mark (?) in the series given below with the correct option.**

4, 5, 7, 11, 19, 35, ?

(a) 67

(b) 76

(c) 55

(d) 45

**Solution: (a)**

In the given series,

Next element = (Previous element × 2 – 3)

**Same Number Multiplication and Subtraction in Increasing Order Subtraction Series**

In this type of series, each previous element is multiplied by a certain number and the from multiplication, numbers in increasing order are subtracted, respectively to obtain each next element.

**Ex 14: What comes in place of question mark (?) in the following number series?**

4, 7, 12, 21, 38, ?

(a) 75

(b) 71

(c) 55

(d) 77

**Solution: (b)**

In the given series, the following pattern is used.

**Increasing Order Multiplication and Same Number Subtraction series**

In this type of series, each previous element is multiplied by numbers in increasing order respectively and then from such multiplications, a certain number is subtracted to obtain each next element.

**Ex 15: What comes is a place of question mark (?) in the following number series?**

4, 6, 16, 62, 308, ?

(a) 990

(b) 1721

(c) 698

(d) 1846

**Solution: (d)**

In the given series, following pattern is used

**Increasing order Multiplication and Increasing Order Subtraction Series**

In this type of series, previous elements are multiplied respectively by numbers in increasing order and then numbers in increasing order are subtracted respectively from such multiplication to obtain the next elements.

**Ex 16: What comes in place of question mark (?) in the following number series?**

3, 5, 13, 49, 241, ?

(a) 1541

(b) 4411

(c) 1600

(d) 1441

**Solution: (d)**

In the given series, following pattern is used.

**Multiplication and Division Series**

In this type of series, each next element is obtained by the operation of multiplication and division alternatively.

**Ex 17: Replace the questions marks (?) in the given series with the suitable option.**

24, 72, 36, 108, 54, ?

(a) 145

(b) 162

(c) 158

(d) 165

**Solution: (b)**

The series pattern is ×3, ÷2, ×3, ÷2 and so on.

**Square series**

In this type of series, each element is the square of a number in a certain sequence.

**Ex: 18 Replace the question mark (?) in the series given below with the suitable option.**

1, 4, 9, 16, 25, 36, ?

(a) 49

(b) 38

(c) 41

(d) 35

**Solution: (a)**

In the given series, following pattern is used

**Cube series**

In this type of series, each element is the cube of a number in a certain sequence.

**Ex: 19 Replace the question mark (?) in the series given below with the suitable option.**

1, 8, 27, 64, 125, ?

(a) 155

(b) 216

(c) 210

(d) 177

**Solution: (b)**

In the series, following pattern is used.

**Square Addition series**

In this type of series, square of numbers in a particular manner are added, respectively to each element to obtain the next element.

**Ex: 20 Replace the question mark (?) in the series given below with the suitable option.**

2,3, 7, 16, 32, ?

(a) 57

(b) 37

(c) 48

(d) 55

**Solution: (a)**

In the given series, following pattern is used

**Cube Addition series**

In this type of series, a cube of a number in a particular manner are added, respectively to each element to obtain the next element.

**Ex21: What comes in place of question mark (?) in the series given below?**

1, 2, 10, 37, 101, ?

(a) 226

(b) 215

(c) 218

(d) 229

**Solution: (a)**

In the given series, the following pattern is used

**Prime Number Series**

In this type of series, each element is prime number in a certain sequence.

**Ex 22: What replace the question mark (?) in the following number series?**

2, 3, 5, 7, 11, ?

(a) 14

(b) 15

(c) 13

(d) 17

**Solution: (c)**

Each next element is the next prime number.

**Digital Operation of Number Series**

In this type of series, the digits of each number are operated in a certain way to obtain the next element of the series.

**Ex 23: What replaces question mark (?) in the series given below?**

88, 64, 24, ?

(a) 8

(b) 6

(c) 2

(d) 5

**Solution: (a)**

In the given series, the following pattern is used.

8 x 8 = 64, 6 x 4 = 24, 2 x 4 = 8

**Mixed /Combination series**

In this type of series, odd place element makes one series while the even place elements make another series.

**Ex 24: Replace the question mark (?) in the following number series.**

5, 25, 7, 22, 9, 19,11,?

(a) 15

(b) 14

(c) 13

(d) 16

**Solution: (d)**

In the given series, the following pattern is used.

## Practice Time:

**1. Direction:** Find the missing number in the following series:

4, 8, 16, 32,_?_,128

- A. 64

B. 46

C. 112

D. 120

**2.** A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.

ACE, GIK, MOQ,?

- A. MUW

B. SUW

C. UVW

D. STV

E. STU

**3.** A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.

LMnP, PQrT, TUvX, ?

- A. VWnP

B. PRsT

C. UVwZ

D. XYzB

**4. **A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.

78, 155, 309, ? , 1233

- A. 625

B. 1230

C. 1000

D. 617

5. **Direction**: Find the missing number in the following series:

36, 34, 30, 28, 24, ?

- A. 23

B. 26

C. 20

D. 22

This article tends to be beneficial for the following exams - REET, UPTET, CTET, Online Classroom Program TET, DSSSB, KVS, etc.

**Suggested Read Books:**

Serial No. | Book Name | Author Name |

1. | A Modern Approach to Verbal & Non-Verbal Reasoning | R.S. Aggarwal |

2. | Quantitative Aptitude for Competitive Examinations | ABHIJIT GUHA and R.S. Aggarwal |

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