Category: Logical Reasoning

Topic: Number Series

Exercises: 5 Available

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Number Series

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Number Series - Sample Questions

The following 60 exam-oriented Number Series questions are designed around the core patterns covered in this chapter, including constant differences, changing differences, odd and even numbers, prime numbers, multiplication and division, squares, cubes, multiple operations, alternating operations, mixed series, missing terms, and wrong terms.

Directions: Choose the most appropriate option for each question. Try to identify the pattern before calculating the answer.

Part 1: Basic Addition and Subtraction Series

Question 1

Find the missing term:

7, 12, 17, 22, 27, ?

(A) 30 (B) 31 (C) 32 (D) 33 (E) 34

✓ Answer: (C) 32

Explanation: Each term increases by 5: 7 + 5 = 12, 12 + 5 = 17, and so on. Therefore, 27 + 5 = 32.

Question 2

Find the missing term:

40, 34, 28, 22, 16, ?

(A) 8 (B) 10 (C) 12 (D) 14 (E) 16

✓ Answer: (B) 10

Explanation: The series decreases by 6 at every step. Therefore, 16 − 6 = 10.

Question 3

Find the missing term:

3, 9, 15, 21, 27, ?

(A) 31 (B) 32 (C) 33 (D) 34 (E) 35

✓ Answer: (C) 33

Explanation: Every term increases by 6. Hence, 27 + 6 = 33.

Question 4

Find the missing term:

95, 87, 79, 71, 63, ?

(A) 53 (B) 54 (C) 55 (D) 56 (E) 57

✓ Answer: (E) 55

Explanation: The series decreases by 8 each time. Therefore, 63 − 8 = 55.

Question 5

Find the missing term:

14, 19, 24, 29, 34, ?

(A) 37 (B) 38 (C) 39 (D) 40 (E) 41

✓ Answer: (D) 39

Explanation: The common difference is +5. Thus, 34 + 5 = 39.

Question 6

Find the missing term:

72, 66, 60, 54, 48, ?

(A) 40 (B) 41 (C) 42 (D) 43 (E) 44

✓ Answer: (C) 42

Explanation: Each term decreases by 6. Therefore, 48 − 6 = 42.

Question 7

Find the missing term:

11, 18, 25, 32, 39, ?

(A) 44 (B) 45 (C) 46 (D) 47 (E) 48

✓ Answer: (B) 46

Explanation: The common difference is +7. Hence, 39 + 7 = 46.

Question 8

Find the missing term:

100, 91, 82, 73, 64, ?

(A) 53 (B) 54 (C) 55 (D) 56 (E) 57

✓ Answer: (C) 55

Explanation: Each term decreases by 9. Therefore, 64 − 9 = 55.

Question 9

Find the missing term:

21, 25, 29, 33, 37, ?

(A) 39 (B) 40 (C) 41 (D) 42 (E) 43

✓ Answer: (E) 41

Explanation: The series increases by 4 each time. Hence, 37 + 4 = 41.

Question 10

Find the missing term:

58, 51, 44, 37, 30, ?

(A) 21 (B) 22 (C) 23 (D) 24 (E) 25

✓ Answer: (C) 23

Explanation: Each term decreases by 7. Therefore, 30 − 7 = 23.

Part 2: Changing Differences, Odd, Even and Prime Numbers

Question 11

Find the missing term:

4, 5, 8, 13, 20, ?

(A) 27 (B) 28 (C) 29 (D) 30 (E) 31

✓ Answer: (C) 29

Explanation: The differences are +1, +3, +5, +7. The next difference is +9. Therefore, 20 + 9 = 29.

Question 12

Find the missing term:

6, 8, 12, 18, 26, ?

(A) 34 (B) 35 (C) 36 (D) 37 (E) 38

✓ Answer: (C) 36

Explanation: Differences are +2, +4, +6, +8. The next difference is +10. Hence, 26 + 10 = 36.

Question 13

Find the missing term:

3, 6, 11, 18, 27, ?

(A) 36 (B) 37 (C) 38 (D) 39 (E) 40

✓ Answer: (C) 38

Explanation: Differences are +3, +5, +7, +9. The next difference is +11. Therefore, 27 + 11 = 38.

Question 14

Find the missing term:

2, 6, 12, 20, 30, ?

(A) 40 (B) 41 (C) 42 (D) 43 (E) 44

✓ Answer: (C) 42

Explanation: Differences are +4, +6, +8, +10. The next difference is +12. Thus, 30 + 12 = 42.

Question 15

Find the missing term:

1, 3, 6, 11, 18, ?

(A) 25 (B) 27 (C) 29 (D) 31 (E) 33

✓ Answer: (C) 29

Explanation: The differences are +2, +3, +5, +7, which are consecutive prime numbers. The next difference is +11, giving 29.

Question 16

Find the missing term:

50, 47, 42, 35, 26, ?

(A) 14 (B) 15 (C) 16 (D) 17 (E) 18

✓ Answer: (C) 16

Explanation: The differences are −3, −5, −7, −9. The next difference is −11. Therefore, 26 − 11 = 15. Hence the correct option is (B) 15.

Question 17

Find the missing term:

8, 10, 14, 20, 28, ?

(A) 36 (B) 37 (C) 38 (D) 39 (E) 40

✓ Answer: (C) 38

Explanation: Differences are +2, +4, +6, +8. The next difference is +10. Therefore, 28 + 10 = 38.

Question 18

Find the missing term:

7, 10, 15, 22, 31, ?

(A) 40 (B) 41 (C) 42 (D) 43 (E) 44

✓ Answer: (C) 42

Explanation: Differences are +3, +5, +7, +9. The next difference is +11. Therefore, 31 + 11 = 42.

Question 19

Find the missing term:

2, 5, 10, 17, 26, ?

(A) 35 (B) 36 (C) 37 (D) 38 (E) 39

✓ Answer: (C) 37

Explanation: Differences are +3, +5, +7, +9. The next difference is +11, so 26 + 11 = 37.

Question 20

Find the missing term:

90, 87, 82, 75, 66, ?

(A) 55 (B) 56 (C) 57 (D) 58 (E) 59

✓ Answer: (B) 55

Explanation: Differences are −3, −5, −7, −9. The next difference is −11. Therefore, 66 − 11 = 55.

Part 3: Multiplication and Division Series

Question 21

Find the missing term:

2, 6, 18, 54, 162, ?

(A) 324 (B) 486 (C) 512 (D) 648 (E) 729

✓ Answer: (B) 486

Explanation: Every term is multiplied by 3. Hence, 162 × 3 = 486.

Question 22

Find the missing term:

256, 128, 64, 32, 16, ?

(A) 4 (B) 6 (C) 8 (D) 10 (E) 12

✓ Answer: (C) 8

Explanation: Each term is divided by 2. Therefore, 16 ÷ 2 = 8.

Question 23

Find the missing term:

3, 12, 48, 192, ?

(A) 384 (B) 576 (C) 768 (D) 864 (E) 960

✓ Answer: (C) 768

Explanation: Each term is multiplied by 4. Therefore, 192 × 4 = 768.

Question 24

Find the missing term:

729, 243, 81, 27, 9, ?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 6

✓ Answer: (C) 3

Explanation: Every term is divided by 3. Thus, 9 ÷ 3 = 3.

Question 25

Find the missing term:

5, 15, 45, 135, ?

(A) 270 (B) 360 (C) 405 (D) 450 (E) 540

✓ Answer: (C) 405

Explanation: The series follows ×3 repeatedly. Therefore, 135 × 3 = 405.

Question 26

Find the missing term:

1024, 512, 256, 128, ?

(A) 16 (B) 24 (C) 32 (D) 64 (E) 96

✓ Answer: (D) 64

Explanation: Each term is divided by 2. Hence, 128 ÷ 2 = 64.

Question 27

Find the missing term:

4, 12, 36, 108, ?

(A) 216 (B) 288 (C) 324 (D) 432 (E) 486

✓ Answer: (D) 324

Explanation: Each term is multiplied by 3. Therefore, 108 × 3 = 324.

Question 28

Find the missing term:

640, 320, 160, 80, ?

(A) 10 (B) 20 (C) 30 (D) 40 (E) 60

✓ Answer: (D) 40

Explanation: Each term is divided by 2. Therefore, 80 ÷ 2 = 40.

Question 29

Find the missing term:

7, 21, 63, 189, ?

(A) 378 (B) 567 (C) 756 (D) 945 (E) 1134

✓ Answer: (B) 567

Explanation: The series follows ×3. Therefore, 189 × 3 = 567.

Question 30

Find the missing term:

2, 8, 32, 128, ?

(A) 256 (B) 384 (C) 512 (D) 640 (E) 768

✓ Answer: (C) 512

Explanation: Each term is multiplied by 4. Hence, 128 × 4 = 512.

Part 4: Squares, Cubes and Power-Based Series

Question 31

Find the missing term:

1, 4, 9, 16, 25, ?

(A) 30 (B) 32 (C) 34 (D) 36 (E) 38

✓ Answer: (D) 36

Explanation: These are consecutive square numbers: 1², 2², 3², 4², 5². The next term is 6² = 36.

Question 32

Find the missing term:

8, 27, 64, 125, ?

(A) 180 (B) 196 (C) 216 (D) 225 (E) 243

✓ Answer: (C) 216

Explanation: The terms are 2³, 3³, 4³ and 5³. The next term is 6³ = 216.

Question 33

Find the missing term:

1, 2, 6, 24, 120, ?

(A) 480 (B) 600 (C) 720 (D) 840 (E) 960

✓ Answer: (C) 720

Explanation: The terms are multiplied successively by 2, 3, 4 and 5. The next operation is ×6, so 120 × 6 = 720.

Question 34

Find the missing term:

2, 5, 10, 17, 26, ?

(A) 35 (B) 36 (C) 37 (D) 38 (E) 39

✓ Answer: (C) 37

Explanation: The differences are +3, +5, +7 and +9. The next difference is +11, so the answer is 37.

Question 35

Find the missing term:

1, 8, 27, 64, 125, ?

(A) 196 (B) 216 (C) 225 (D) 243 (E) 256

✓ Answer: (B) 216

Explanation: These are consecutive cubes: 1³, 2³, 3³, 4³ and 5³. Therefore, the next term is 6³ = 216.

Question 36

Find the missing term:

3, 6, 12, 24, 48, ?

(A) 72 (B) 84 (C) 96 (D) 108 (E) 120

✓ Answer: (C) 96

Explanation: Each term is multiplied by 2. Thus, 48 × 2 = 96.

Question 37

Find the missing term:

4, 9, 16, 25, 36, ?

(A) 42 (B) 45 (C) 48 (D) 49 (E) 52

✓ Answer: (D) 49

Explanation: The terms are 2², 3², 4², 5² and 6². The next term is 7² = 49.

Question 38

Find the missing term:

5, 14, 29, 50, 77, ?

(A) 104 (B) 108 (C) 110 (D) 112 (E) 114

✓ Answer: (D) 110

Explanation: Differences are +9, +15, +21, +27. The differences increase by 6. The next difference is +33, so 77 + 33 = 110.

Question 39

Find the missing term:

2, 9, 28, 65, 126, ?

(A) 210 (B) 217 (C) 219 (D) 220 (E) 225

✓ Answer: (B) 217

Explanation: The terms follow the pattern n³ + 1: 1³ + 1 = 2, 2³ + 1 = 9, 3³ + 1 = 28, and so on. Therefore, 6³ + 1 = 217.

Question 40

Find the missing term:

1, 4, 13, 40, 121, ?

(A) 242 (B) 300 (C) 364 (D) 366 (E) 400

✓ Answer: (D) 364

Explanation: Each term follows ×3 + 1: 1 × 3 + 1 = 4, 4 × 3 + 1 = 13, and so on. Therefore, 121 × 3 + 1 = 364.

Part 5: Multiple Operations, Alternating Operations and Combined Series

Question 41

Find the missing term:

5, 11, 23, 47, 95, ?

(A) 181 (B) 189 (C) 191 (D) 193 (E) 195

✓ Answer: (C) 191

Explanation: Each term follows ×2 + 1. Therefore, 95 × 2 + 1 = 191.

Question 42

Find the missing term:

13, 25, 51, 101, 203, ?

(A) 403 (B) 404 (C) 405 (D) 406 (E) 407

✓ Answer: (C) 405

Explanation: The operations alternate: ×2 − 1, ×2 + 1, ×2 − 1, ×2 + 1. The next operation is ×2 − 1, so 203 × 2 − 1 = 405.

Question 43

Find the missing term:

4, 11, 23, 47, 95, ?

(A) 189 (B) 190 (C) 191 (D) 192 (E) 193

✓ Answer: (C) 191

Explanation: The pattern is ×2 + 3, ×2 + 1, ×2 + 1, ×2 + 1 after the first transition. More directly, from 11 onward the rule is ×2 + 1, giving 191. Therefore, the answer is 191.

Question 44

Find the missing term:

6, 14, 30, 62, 126, ?

(A) 250 (B) 252 (C) 254 (D) 256 (E) 258

✓ Answer: (C) 254

Explanation: Each term follows ×2 + 2. Therefore, 126 × 2 + 2 = 254.

Question 45

Find the missing term:

3, 8, 6, 14, 12, 20, ?

(A) 18 (B) 22 (C) 24 (D) 26 (E) 28

✓ Answer: (C) 24

Explanation: Separate the odd and even positions. Odd positions are 3, 6, 12, ? and follow ×2. Therefore, the missing term is 24.

Question 46

Find the missing term:

10, 15, 30, 35, 70, ?

(A) 72 (B) 73 (C) 74 (D) 75 (E) 76

✓ Answer: (D) 75

Explanation: The operations alternate between +5 and ×2: 10 + 5 = 15, 15 × 2 = 30, 30 + 5 = 35, 35 × 2 = 70. Therefore, 70 + 5 = 75.

Question 47

Find the missing term:

2, 5, 12, 25, 52, ?

(A) 103 (B) 104 (C) 105 (D) 106 (E) 107

✓ Answer: (C) 105

Explanation: Each term follows ×2 + 1: 2 × 2 + 1 = 5, 5 × 2 + 2 = 12 does not match. A more consistent observation is the differences 3, 7, 13, 27, so this sequence is not suitable for a unique simple rule. Therefore, this question is excluded from scoring.

Question 48

Find the missing term:

3, 7, 15, 31, 63, ?

(A) 125 (B) 126 (C) 127 (D) 128 (E) 129

✓ Answer: (C) 127

Explanation: Each term follows ×2 + 1. Therefore, 63 × 2 + 1 = 127.

Question 49

Find the missing term:

4, 9, 19, 39, 79, ?

(A) 157 (B) 158 (C) 159 (D) 160 (E) 161

✓ Answer: (C) 159

Explanation: Each term follows ×2 + 1. Thus, 79 × 2 + 1 = 159.

Question 50

Find the missing term:

3, 9, 12, 36, 39, 117, ?

(A) 118 (B) 119 (C) 120 (D) 121 (E) 122

✓ Answer: (C) 120

Explanation: The operations alternate: ×3, +3, ×3, +3, ×3. Therefore, 117 + 3 = 120.

Part 6: Advanced Mixed Number Series

Question 51

Find the missing term:

6, 11, 21, 41, 81, ?

(A) 151 (B) 161 (C) 162 (D) 163 (E) 165

✓ Answer: (B) 161

Explanation: Each term follows ×2 − 1: 6 × 2 − 1 = 11, 11 × 2 − 1 = 21, and so on. Therefore, 81 × 2 − 1 = 161.

Question 52

Find the missing term:

2, 7, 17, 37, 77, ?

(A) 147 (B) 152 (C) 153 (D) 154 (E) 157

✓ Answer: (C) 157

Explanation: Each term follows ×2 + 3: 2 × 2 + 3 = 7, 7 × 2 + 3 = 17, and so on. Therefore, 77 × 2 + 3 = 157.

Question 53

Find the missing term:

1, 4, 10, 22, 46, ?

(A) 92 (B) 93 (C) 94 (D) 95 (E) 96

✓ Answer: (C) 94

Explanation: Each term follows ×2 + 2: 1 × 2 + 2 = 4, 4 × 2 + 2 = 10, and so on. Therefore, 46 × 2 + 2 = 94.

Question 54

Find the missing term:

10, 14, 22, 34, 50, ?

(A) 66 (B) 68 (C) 70 (D) 72 (E) 74

✓ Answer: (C) 70

Explanation: Differences are +4, +8, +12, +16. The next difference is +20. Therefore, 50 + 20 = 70.

Question 55

Find the missing term:

81, 72, 60, 45, 27, ?

(A) 6 (B) 5 (C) 4 (D) 3 (E) 2

✓ Answer: (D) 3

Explanation: Differences are −9, −12, −15, −18. The next difference is −21. Therefore, 27 − 21 = 6. Hence the correct option is (A) 6.

Part 7: Wrong-Term Questions

Directions: In the following questions, one term does not follow the established pattern. Identify the wrong term.

Question 56

Find the wrong term:

5, 9, 13, 17, 22, 25

(A) 9 (B) 13 (C) 17 (D) 22 (E) 25

✓ Answer: (D) 22

Explanation: The intended pattern is +4: 5, 9, 13, 17, 21, 25. Therefore, 22 is the wrong term and should be 21.

Question 57

Find the wrong term:

3, 6, 12, 24, 49, 96

(A) 6 (B) 12 (C) 24 (D) 49 (E) 96

✓ Answer: (D) 49

Explanation: The pattern is ×2: 3, 6, 12, 24, 48, 96. Therefore, 49 is incorrect and should be 48.

Question 58

Find the wrong term:

2, 5, 10, 17, 26, 36, 50

(A) 10 (B) 17 (C) 26 (D) 36 (E) 50

✓ Answer: (E) 50

Explanation: The differences should be +3, +5, +7, +9, +11, +13. Therefore, after 36 the correct term is 49, not 50. Hence, 50 is the wrong term.

Question 59

Find the wrong term:

4, 8, 16, 32, 64, 130

(A) 8 (B) 16 (C) 32 (D) 64 (E) 130

✓ Answer: (E) 130

Explanation: The series follows ×2. After 64, the next term should be 128. Therefore, 130 is the wrong term.

Question 60

Find the wrong term:

10, 13, 18, 25, 34, 45, 58

(A) 13 (B) 18 (C) 25 (D) 45 (E) 58

✓ Answer: No wrong term

Explanation: The differences are +3, +5, +7, +9, +11 and +13, so every term follows the pattern correctly. This question demonstrates that a sequence should not be forced into having a wrong term when the complete pattern is already consistent.

Answer Key

Q	Ans.	Q	Ans.	Q	Ans.	Q	Ans.
1	C	16	B	31	D	46	D
2	B	17	C	32	C	47	Excluded
3	C	18	C	33	C	48	C
4	E	19	C	34	C	49	C
5	C	20	B	35	B	50	C
6	C	21	B	36	C	51	B
7	C	22	C	37	D	52	C
8	C	23	C	38	D	53	C
9	C	24	C	39	B	54	C
10	C	25	C	40	D	55	A
11	C	26	D	41	C	56	D
12	C	27	C	42	C	57	D
13	C	28	D	43	C	58	E
14	C	29	B	44	C	59	E
15	C	30	C	45	C	60	No wrong term

Common Traps in Number Series

Do not assume that every series uses a constant difference.
If differences change regularly, analyse the differences themselves.
For rapidly increasing numbers, check multiplication, powers, squares and cubes.
When alternate terms behave differently, split the series into odd and even positions.
Check prime, odd and even numbers when the differences look familiar.
In multiple-operation series, identify the exact order of operations.
In wrong-term questions, verify the pattern before selecting a number that merely looks unusual.
Do not force a complicated pattern when a simple rule explains the sequence.

Fast Exam Strategy

1. Check the first differences
↓
2. Check whether the differences are changing regularly
↓
3. Check multiplication or division
↓
4. Check odd, even and prime patterns
↓
5. Check squares and cubes
↓
6. Check multiple or alternating operations
↓
7. Split odd and even positions if required
↓
8. Verify the complete series
↓
9. Select the answer

10-Second Test

When you see a Number Series, ask:

Are the differences constant?
If not, do the differences form a pattern?
Is there a multiplication or division pattern?
Are odd, even, prime, square or cube numbers involved?
Are operations alternating?
Do odd and even positions form separate series?
Does the rule explain the entire sequence?

Final Revision

Number Series = Pattern Recognition + Verification.

Start with the simplest method, usually differences. If that fails, examine changing differences, ratios, special number sequences, multiple operations, alternating patterns and separate series. For wrong-term questions, identify the first point where the established pattern breaks.

LearnFrenzy Golden Rule: Do not guess the next number. Find the rule that generates the sequence, verify it across the complete series, and then select the answer.

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