## Introduction

To solve the problems related to sequences and series, we need to identify the pattern being followed in the sequence or series of alphabets/numbers. Based on that, we can be asked to find the missing term(s) in the series, find the nth term in the series or identify the wrong term within the series.

You will learn to identify the patterns as you practice more and more questions.

### Practice Exercise 1: Find the wrong term in the following number series.

4 , 5.1 , 7.3 , 10.6 , 15 , 20 , 27.1

A. 7.3

B. 20

C. 27.1

D. 4

E. 15

4 + 1.1 = 5.1

5.1 + 2.2 = 7.3

7.3 + 3.3 = 10.6

10.6 + 4.4 = 15

15 + 5.5 = 20.5 ≠ 20

20.5 + 6.6 = 27.1

Therefore, 20 is the wrong term. So, B is the correct option.

### Practice Exercise 2: What should come in place of question mark (?) in the following number series?

18 , 20 , 16 , 24 , (?) , 40

A. 64

B. 32

C. 8

D. 16

E. 4

18 + 2 = 20

20 – 22 = 16

16 + 23 = 24

24 – 24 = 8

8 + 25 = 40

Therefore, the missing term is 8. So, C is the correct option.

### Practice Exercise 3: Find the wrong term in the following number series.

2 , 3 , 8 , 31 , 154 , 924 , 6460

A. 3

B. 31

C. 154

D. 924

E. 6460

2 × 2 – 1 = 3

3 × 3 – 1 = 8

8 × 4 – 1 = 31

31 × 5 – 1 = 154

154 × 6 – 1 = 923 ≠ 924

923 × 7 – 1 = 6460

Therefore, 924 is the wrong term. So, D is the correct option.

### Practice Exercise 4: Find out the next number in place of question mark (?) in the following number series.

14 , 28 , 84 , 336 , (?)

A. 1800

B. 1780

C. 1728

D. 1680

E. None of these

14 × 2 = 28

28 × 3 = 84

84 × 4 = 336

336 × 5 = 1680

Therefore, the next term is 1680. So, D is the correct option.

### Practice Exercise 5: Find the wrong term in the following number series.

2 , 6 , 10 , 19 , 36 , 69 , 134

A. 36

B. 19

C. 10

D. 6

E. 2

We can recognize the pattern by observing the last 4 terms: 19 , 36 , 69 , 134.

2 × 2 + 1 = 5 ≠ 6

5 × 2 + 0 = 10

10 × 2 – 1 = 19

19 × 2 – 2 = 36

36 × 2 – 3 = 79

69 × 2 -4 = 134

Therefore, 6 is the wrong term. So, D is the correct option.

### Practice Exercise 6: What should come in place of question mark (?) in the following number series?

3 , 7 , 19 , 39 , (?) , 103

A. 49

B. 51

C. 53

D. 67

E. 63

Let’s check the difference between consecutive terms.

7 – 3 = 4

19 – 7 = 12 = 4 × 3

39 – 19 = 20 = 4 × 5

Following this pattern,

the next term = 39 + 4 × 7 = 67

67 + 4 × 9 = 103

Therefore, the missing term is 67. So, D is the correct option.

### Practice Exercise 7: Find the wrong term in the following number series.

0.5 , 2 , 1 , 4 , 32 , 512

A. 0.5

B. 2

C. 4

D. 32

E. 512

Taking from the opposite side

512 ÷ 24 = 32

32 ÷ 23 = 4

4 ÷ 22 = 1

1 ÷ 21 = 0.5 ≠ 2

0.5 ÷ 20 = 0.5

Therefore, 2 is the wrong term. So, B is the correct option.

### Practice Exercise 8: Find the next term in place of question mark (?) in the following number series.

11 , 15 , 31 , 67 , 131 , (?)

A. 121

B. 161

C. 231

D. 151

E. 1625

11 + 22 = 15

15 + 42 = 31

31 + 62 = 67

67 + 82 = 131

131 + 102 = 231

Therefore, the next term is 231. So, C is the correct option.

### Practice Exercise 9: Find the wrong term in the following number series.

251 , 252 , 254 , 227 , 243 , 118 , 154

A. 251

B. 252

C. 254

D. 227

E. 118

Observe the last 5 terms:

254 – 33 = 227

227 + 42 = 243

243 – 53 = 118

118 + 62 = 154

Following this pattern,

the second term = 251 – 13 = 250 ≠ 252

Therefore, 252 is the wrong term. So, B is the correct option.

### Practice Exercise 10: Find the next term in place of question mark (?) in the following number series.

10 ,40 , 60 , 72 , 78, (?)

A. 86

B. 84

C. 80

D. 98

E. None of these

Let’s check the difference between consecutive terms.

40 – 10 = 30

60 – 40 = 20

72 – 60 = 12

78 – 72 = 6

Now, 30 = 5 × 6

20 = 4 × 5

12 = 3 × 4

6 = 2 × 3

Following this pattern, next difference = 1 × 2 = 2

Therefore, the next term = 78 + 2 = 80. So, C is the correct answer.