Number Series - Reasoning Questions and Answers

🧠 Number Series – Logical Reasoning for Competitive Exams

Number Series is one of the most frequently asked topics in the Logical Reasoning section of various competitive exams in India, such as SSC, Bank, UPSC, and others. In these questions, you’re presented with a sequence of numbers where one term is missing. Your task is to identify the pattern or rule governing the sequence and find the missing number.

While the question format may seem simple, the real challenge lies in cracking the logic behind the pattern—making this an important skill to master for scoring well.

📘 What You’ll Learn

How to identify patterns in number series
Tricks to solve missing number and wrong number problems
Key types of series seen in exams
Practice with solved examples and explanations

🔍 Common Patterns in Number Series

✅ Increasing Difference Series
- Each number increases by a larger amount than the previous one.
✅ Constant Difference Series
- Each term increases or decreases by the same fixed number.
✅ Decreasing Difference Series
- The gap between terms reduces in a pattern.
✅ Square and Cube-Based Series
- Involves perfect squares or cubes—either directly or through operations.
✅ Mixed Operation Series
- Combines operations like addition, subtraction, multiplication, division, or powers.

📚 Why Practice Number Series?

Sharpens logical thinking and pattern recognition
Frequently appears in aptitude tests
Helps improve speed and accuracy in exams
Enhances problem-solving skills under time pressure

Ready to master number series questions? 🚀
Start practicing with our solved examples and quizzes to boost your exam performance!

Solved Examples on Number Series

Find the missing term.

Q1. Given a Series 2, 5, 12.5, ?, 78.125, 195.3125
Find what number would come in place of the question mark(?).

a) 31.25

b) 40.25

c) 32.50

d) 21.00

Answer : (a) 31.25

Explanation

If you observe the pattern, then you can see

2 × 2.5 = 5
5 × 2.5 = 12.5
12.5 × 2.5 = 31.25
31.25 × 2.5 = 78.125
78.125 × 2.5 = 195.3125

Hence, the correct answer is 31.25

Q2. Given a Series 50, 45, 40, 35, 30, ?
Find what number would come in place of the question mark(?).

a) 28

b) 15

c) 25

d) 20

Answer : (c) 25

Explanation :

If you observe the pattern, then you will see, it’s nothing but constant difference series.

50 – 5 = 45
45 – 5 = 40
40 – 5 = 35
35 – 5 = 30
30 – 5 = 25

Hence, the correct answer is 25.

Q3. Given a Series -10, -8, 6, 40, 102, ?
Find what number would come in place of the question mark(?).

a) 105

b) 200

c) 216

d) 129

Answer : (b) 200

Explanation:

Observing patterns carefully you will find that this question belongs to the category of square series.

-10 + ( 2²– 2 ) = -8
-8 + ( 4²– 2 ) = 6
6 + ( 6²– 2 ) = 40
40 + ( 8²– 2 ) = 102
102 + ( 10²– 2 ) = 200

Hence, the correct answer is 200.

Q4. Given a Series 25, 49, 121, 169,?
Find what number would come in place of the question mark(?).

a) 225

b) 256

c) 289

d) 361

Answer: (c) 289

Explanation:-

Observing patterns carefully, you will observe that, this series is based on two concepts one is squares and the other is a prime number.

5² = 25
7² = 49
11²= 121
13² = 169
17² = 289

Hence, the correct answer is 289

Q5. Given a Series 1, 30, 5, 26, 9, 22, 13, 18, ?
Find what number would come in place of the question mark(?).

a) 17

b) 22

c) 28

d) 19

Answer : (a) 17

Explanation:-

Observing the pattern carefully, you will observe that, this series consist of 2 different series.

Let me point out them for ease of understanding —
1 + 4 = 5
5 + 4 = 9
9 + 4 = 13
13+4= 17.

Similarly,

30 – 4 = 26
26 – 4 = 22
22 – 4 =18

Q6. Find the number that will come in the place of the question mark in the given series 4, 18, ?, 100, 180, 294, 448.

a) 62

b) 86

c) 38

d) 48

Answer : (d) 48

Explanation:-
Observing pattern carefully you will find that this question belongs to the category of squares and cube series.

2³ – 2² = 8 – 4 = 4
3³ – 3² = 27 – 9 = 18
4³ – 4² = 64 – 16 = 48
5³ – 5² = 125 – 25 = 100
6³ – 6² = 216 – 36 = 180
7³ – 7² = 343 – 49 = 294
8³ – 8² = 512 – 64 = 448

Hence 48 would be our answer, as it is the number that would come in place of a question mark.

Q7. Find the number that will come in the place of the question mark in the given series 11, 12, 15, 20, 27, ?

a) 36

b) 35

c) 38

d) 41

Answer : (a) 36

Explanation:-

Here, the series follows a pattern of the sum of consecutive odd numbers.

11 + 1 = 12
12 + 3 = 15
15 + 5 = 20
20 + 7 = 27
27 + 9 = 36.

Hence, the missing number would be 36.

Q8. Find the number that will come in the place of the question mark in the given series 14, 25, 47, 91, 179, ?.

a) 255

b) 321

c) 355

d) 211

Answer : (c) 355

Explanation:-

observing the pattern we get that the difference between consecutive terms is being doubled every time.

25 – 14 = 11
47 – 25 = 22
91 – 47 = 44
179 – 91 = 88

So, if 88 is doubled, we get 176.

Hence, 179 + 176 = 355
Hence the missing term is 355.

Q9. Find the number that will come in the place of the question mark in the given series 4, 6, 9, 14, 21, ?.

a) 28

b) 32

c) 34

d) 40

Answer : (b) 32

Explanation:-

Observing the pattern, one can easily come to know that, the difference between consecutive terms is a prime number.

4 + 2 = 6
6 + 3 = 9
9 + 5 = 14
14 + 7 = 21
21 + 11 = 32.

Hence, the missing number will be 32.

Q10. Find the number which would come in place of question marks 3, 4, 7, 8, 11, 12, ?, ?.

a) 13, 14

b) 18, 20

c) 15, 16

d) 19, 20

Answer : (c) 15, 16

Explanation:-

This is a Hybrid series, which is formed from the combination of two series i.e 3,7,11,…. and 4,8, 12.
So, the difference between every term in different series is 4. hence 11 + 4 would be the next term i.e 15
and 12 + 4 =16 is the further next term.

Q11. Find the number which is wrong in the given series 2, 3, 12, 37, 86, 166, 288.

a) 2

b) 12

c) 37

d) 166

Answer : (d) 166

Explanation:-

Observing the pattern carefully, every term is formed from a sum of (the previous term and consecutive odd number squares).

2 + 1² = 2 + 1 = 3
3 + 3² = 3 + 9 = 12
12 + 5² = 12 + 25 = 37
37 + 7² = 37 + 49 = 86
86 + 9² = 86 + 81 = 167
167 + 11² = 167 + 121 = 288.

Clearly, we can see that 167 should be there instead of 166. Hence 166 is the wrong term.

Q12. Find the number which would come in place of question mark 81 : 101 :: 121 : ? .

a) 141

b) 143

c) 170

d) 145

Answer : (d) 145

Explanation:-

Here 81 is nothing but 9² and 101 is nothing but (9 + 1)² +1

So, likewise this
121 is nothing but 11²
so ,next term will be (11 + 1)² + 1 = 145

Q13. Find the number which would come in place of question mark 11 : 121 :: 15 : ?

a) 169

b) 196

c) 225

d) 256

Answer : (c) 225

Explanation:-

Observing pattern we get,
Here, 11² = 121
So, 15²= 225

So, the missing number is 225.

Q14. Find the number which would come in place of question mark 2, 4, 8, 10, 14, ?.

a) 16

b) 18

c) 24

d) 20

Answer : (a) 16

Explanation:-

This series is an alternating series, where a pattern following is +2, +4, +2, +4, and so on

2 + 2 = 4
4 + 4 = 8
8 + 2 = 10
10 + 4 = 14
14 + 2 = 16

Hence the next term will be 16.

Q15. Find the number which would come in place of question mark 1, 8, 9, 64, ?.

a) 27

b) 49

c) 25

d) 64

Answer : (c) 25

Explanation:-

Observing carefully one can come to know that this series is nothing but squares and cubes of numbers starting from 1

1² = 1
2³ = 8
3² = 9
4³ = 64
5² = 25

Hence, 25 will be the answer.

Q16. Find the number which would come in place of question mark 6, 11, 18, 27, ?.

a) 33

b) 40

c) 38

d) 81

Answer : (c) 38

Explanation:-

Here, every term is squares from (starting from 2 ) with the addition of 2.

2² + 2 = 6
3² + 2 =11
4² + 2 = 18
5² + 2 = 27
6² + 2 = 38

Q17. Find the number which would come in place of question mark 3, 4.5, 9, ?

a) 22.5

b) 18

c) 13.5

d) 27

Answer : (a) 22.5

Explanation:-

This series is a product based, below is the pattern for finding the next term

3 × 1 = 3
3 × 1.5 = 4.5
4.5 × 2 = 9
9 × 2.5 = 22.5

Hence, 22.5 will be our answer.

Q18. Find the number which would come in place of question mark 3, 5, 7, 9, 11, ?,

a) 13

b) 17

c) 19

d) 12

Answer : (a) 13

Explanation:-

It can be seen in 2 ways,

1. it is simple just a difference of 2 in every consecutive term that is —

3 + 2 = 5
5 + 2 = 7
7 + 2 = 9
9 + 2 = 11
11 + 2 = 13. Hence 13 will be the answer.

2. It can also be seen as a difference of squares of numbers –

2² – 1² = 3
3² – 2² = 5
4² – 3² = 7
5² – 4² = 9
6² – 5² = 11
7² – 6² = 13. Hence 13, will be the answer.

Q19. Find the number which would come in place of question mark 1, 7, 37, 187, 937, ?.

a) 4687

b) 1823

c) 5687

d) 5000

Answer : (a) 4687

Explanation:-

Here, every term is multiplied by 5, and adding 2 to get the next term of the series.

1 × 5 + 2 = 7
7 × 5 + 2 = 37
37 × 5 + 2 = 187
187 × 5 + 2 = 937
937 × 5 + 2 = 4687

Hence, 4867 will be our answer.

Q20. Find the number which would come in place of question mark 1, 5, 19, 81, ?

a) 405

b) 411

c) 400

d) 395

Answer : (b) 411

Explanation:-

Below is the pattern to crack this series

1 × 2 + 3 = 5
5 × 3 + 4 = 19
19 × 4 + 5 = 81
81 × 5 + 6 = 411

Hence, 411 will be our answer.