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 n^{th} 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 – 2^{2} = 16

16 + 2^{3} = 24

24 – 2^{4} = 8

8 + 2^{5} = 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 ÷ 2^{4} = 32

32 ÷ 2^{3} = 4

4 ÷ 2^{2} = 1

1 ÷ 2^{1} = 0.5 ≠ 2

0.5 ÷ 2^{0} = 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 + 2^{2} = 15

15 + 4^{2} = 31

31 + 6^{2} = 67

67 + 8^{2} = 131

131 + 10^{2} = 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 – 3^{3} = 227

227 + 4^{2} = 243

243 – 5^{3} = 118

118 + 6^{2} = 154

Following this pattern,

the second term = 251 – 1^{3} = 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.