Fibonacci Series
The Fibonacci Series is one of the most important number-series patterns in reasoning. In this pattern, each number is formed by adding the previous two numbers.
Formula:
F_n=F_{n-1}+F_{n-2}
This means:
Next term = Previous term + Term before previous
Basic Fibonacci Series
0, 1, 1, 2, 3, 5, 8, 13, 21, 34 …
Check:
0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
Example 1
2, 3, 5, 8, 13, 21, ?
Check:
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
Answer = 34
Example 2
1, 4, 5, 9, 14, 23, ?
Check:
1 + 4 = 5
4 + 5 = 9
5 + 9 = 14
9 + 14 = 23
14 + 23 = 37
Answer = 37
Modified Fibonacci Pattern
Sometimes exams use:
- addition/subtraction with Fibonacci,
- multiplication with Fibonacci,
- alternate Fibonacci patterns.
Example
2, 6, 8, 14, 22, 36, ?
Check:
2 + 6 = 8
6 + 8 = 14
8 + 14 = 22
14 + 22 = 36
Next:
22 + 36 = 58
Answer = 58
How to Identify Quickly in Exams
Check whether:
- a number equals the sum of previous two numbers,
- numbers grow naturally,
- differences do not follow a simple pattern.
Exam Trick
If:
- addition pattern fails,
- multiplication fails,
- but terms seem connected,
then immediately test:
Previous two terms added together.
Important Points
- Fibonacci questions are very common in SSC, Banking, Railways, and other exams.
- Sometimes the series starts from different numbers.
- The logic remains the same:
Next term = sum of previous two terms
Learning Fibonacci patterns improves speed in reasoning number series.
Alternative/Mixed Number Series
Alternative/Mixed Number Series is one of the most common and tricky topics in reasoning. In this type, the pattern changes between two different logics.
Usually:
- odd-position numbers follow one pattern,
- even-position numbers follow another pattern.
So, instead of checking the whole series together, divide it into two groups.
1. Alternative Pattern
Example
2, 5, 4, 10, 6, 15, 8, ?
Separate positions:
Odd positions:
2, 4, 6, 8 → +2
Even positions:
5, 10, 15, ? → +5
Next even term:
15 + 5 = 20
Answer = 20
2. Another Example
1, 3, 4, 9, 7, 27, 10, ?
Odd positions:
1, 4, 7, 10 → +3
Even positions:
3, 9, 27, ? → ×3
27 × 3 = 81
Answer = 81
3. Mixed Pattern
In mixed series, more than one operation is used:
- addition + multiplication,
- square + subtraction,
- Fibonacci + multiplication, etc.
Example
2, 5, 11, 23, 47, ?
Pattern:
2 × 2 + 1 = 5
5 × 2 + 1 = 11
11 × 2 + 1 = 23
23 × 2 + 1 = 47
Next:
47 × 2 + 1 = 95
Answer = 95
4. Another Mixed Example
3, 6, 18, 72, 360, ?
Pattern:
3 × 2 = 6
6 × 3 = 18
18 × 4 = 72
72 × 5 = 360
Next:
360 × 6 = 2160
Answer = 2160
How to Identify Alternative/Mixed Series
If:
- simple addition/subtraction fails,
- differences look irregular,
- terms at alternate positions seem related,
then check:
- odd/even positions separately,
- mixed operations.
Exam Trick
Always check in this order:
- Addition/Subtraction
- Multiplication/Division
- Step difference
- Odd-even pattern
- Mixed operations
- Squares/Cubes/Fibonacci
Final Tip
Alternative and mixed series are very common in SSC, Banking, Railways, and other competitive exams. The key is:
- do not panic,
- split the series carefully,
- identify separate patterns step by step.
Illogical Series
An Illogical Series is a number series where the numbers do not follow any proper mathematical pattern like addition, subtraction, multiplication, squares, cubes, Fibonacci, etc. In competitive exams, these questions are usually asked to test whether you can identify the wrong or odd term in the series.
In this type:
- most numbers follow a pattern,
- but one number breaks the pattern,
- and that number is called the illogical term or wrong number.
Example 1
2, 4, 8, 16, 31, 64
Check pattern:
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
32 × 2 = 64
But series has 31 instead of 32.
So, 31 is the illogical/wrong term.
Example 2
3, 6, 12, 24, 49, 96
Pattern should be:
3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
24 × 2 = 48
48 × 2 = 96
But series has 49.
So, 49 is the wrong term.
Example 3
1, 4, 9, 15, 25, 36
Check square numbers:
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
But series has 15 instead of 16.
So, 15 is the illogical term.
How to Solve Quickly
Check patterns in this order:
- Addition/Subtraction
- Multiplication/Division
- Squares/Cubes
- Prime numbers
- Fibonacci
- Alternative patterns
Find the number that does not fit the pattern.
Common Types of Illogical Series
- Wrong multiplication
- Wrong square/cube
- Missing Fibonacci logic
- Incorrect alternate term
- One term added/subtracted wrongly
Exam Trick
If only one number looks strange:
- do not change the entire pattern,
- check whether all other terms follow one rule,
- identify the single wrong term.
50 Practice MCQs
1. 2, 5, 8, 11, 14, ?
A. 15
B. 16
C. 17
D. 18
Answer: C. 17
Explanation: Add 3 each time.
2 + 3 = 5
5 + 3 = 8
8 + 3 = 11
14 + 3 = 17
2. 30, 27, 24, 21, 18, ?
A. 12
B. 15
C. 16
D. 17
Answer: B. 15
Explanation: Subtract 3 each time.
30 − 3 = 27
27 − 3 = 24
18 − 3 = 15
3. 2, 4, 8, 16, 32, ?
A. 48
B. 56
C. 64
D. 72
Answer: C. 64
Explanation: Multiply by 2 each time.
2 × 2 = 4
4 × 2 = 8
32 × 2 = 64
4. 128, 64, 32, 16, 8, ?
A. 2
B. 4
C. 6
D. 8
Answer: B. 4
Explanation: Divide by 2 each time.
128 ÷ 2 = 64
64 ÷ 2 = 32
8 ÷ 2 = 4
5. 1, 4, 9, 16, 25, ?
A. 35
B. 36
C. 37
D. 38
Answer: B. 36
Explanation: Perfect square numbers.
1² = 1
2² = 4
3² = 9
6² = 36
6. 1, 8, 27, 64, 125, ?
A. 196
B. 206
C. 216
D. 226
Answer: C. 216
Explanation: Perfect cube numbers.
1³ = 1
2³ = 8
3³ = 27
6³ = 216
7. 2, 6, 12, 20, 30, ?
A. 40
B. 41
C. 42
D. 43
Answer: C. 42
Explanation: Pattern is n² + n.
1² + 1 = 2
2² + 2 = 6
6² + 6 = 42
8. 0, 6, 24, 60, 120, ?
A. 180
B. 190
C. 200
D. 210
Answer: D. 210
Explanation: Pattern is n³ − n.
1³ − 1 = 0
2³ − 2 = 6
6³ − 6 = 210
9. 2, 5, 11, 23, 47, ?
A. 91
B. 93
C. 95
D. 97
Answer: C. 95
Explanation: Multiply by 2 and add 1.
2 × 2 + 1 = 5
5 × 2 + 1 = 11
47 × 2 + 1 = 95
10. 1, 1, 2, 3, 5, ?
A. 6
B. 7
C. 8
D. 9
Answer: C. 8
Explanation: Fibonacci series.
1 + 1 = 2
1 + 2 = 3
3 + 5 = 8
11. 3, 6, 9, 12, 15, ?
A. 16
B. 17
C. 18
D. 19
Answer: C. 18
Explanation: Add 3 each time.
15 + 3 = 18
12. 50, 45, 40, 35, 30, ?
A. 20
B. 25
C. 26
D. 27
Answer: B. 25
Explanation: Subtract 5 each time.
30 − 5 = 25
13. 3, 9, 27, 81, ?
A. 162
B. 243
C. 324
D. 729
Answer: B. 243
Explanation: Multiply by 3 each time.
81 × 3 = 243
14. 256, 128, 64, 32, ?
A. 8
B. 12
C. 16
D. 24
Answer: C. 16
Explanation: Divide by 2 each time.
32 ÷ 2 = 16
15. 4, 9, 16, 25, 36, ?
A. 47
B. 48
C. 49
D. 50
Answer: C. 49
Explanation: Perfect squares.
2² = 4
3² = 9
7² = 49
16. 8, 27, 64, 125, ?
A. 196
B. 216
C. 256
D. 343
Answer: B. 216
Explanation: Perfect cubes.
2³ = 8
3³ = 27
6³ = 216
17. 0, 2, 6, 12, 20, ?
A. 24
B. 28
C. 30
D. 32
Answer: C. 30
Explanation: Pattern is n² − n.
1² − 1 = 0
2² − 2 = 2
6² − 6 = 30
18. 2, 10, 30, 68, 130, ?
A. 180
B. 210
C. 222
D. 240
Answer: C. 222
Explanation: Pattern is n³ + n.
1³ + 1 = 2
2³ + 2 = 10
6³ + 6 = 222
19. 15, 10, 20, 40, 80, ?
A. 120
B. 140
C. 160
D. 320
Answer: C. 160
Explanation: Multiply by 2 each time.
80 × 2 = 160
20. 2, 3, 5, 8, 13, ?
A. 18
B. 19
C. 20
D. 21
Answer: D. 21
Explanation: Fibonacci series.
2 + 3 = 5
3 + 5 = 8
8 + 13 = 21
21. 7, 10, 13, 16, 19, ?
A. 20
B. 21
C. 22
D. 23
Answer: C. 22
Explanation: Add 3 each time.
19 + 3 = 22
22. 100, 90, 80, 70, ?
A. 50
B. 55
C. 60
D. 65
Answer: C. 60
Explanation: Subtract 10 each time.
70 − 10 = 60
23. 5, 15, 45, 135, ?
A. 270
B. 315
C. 405
D. 425
Answer: C. 405
Explanation: Multiply by 3 each time.
135 × 3 = 405
24. 81, 27, 9, 3, ?
A. 1
B. 2
C. 4
D. 6
Answer: A. 1
Explanation: Divide by 3 each time.
3 ÷ 3 = 1
25. 9, 16, 25, 36, 49, ?
A. 60
B. 61
C. 64
D. 81
Answer: C. 64
Explanation: Perfect square numbers.
3² = 9
4² = 16
8² = 64
26. 27, 64, 125, 216, ?
A. 256
B. 343
C. 512
D. 729
Answer: B. 343
Explanation: Perfect cubes.
3³ = 27
4³ = 64
7³ = 343
27. 2, 8, 18, 32, 50, ?
A. 60
B. 70
C. 72
D. 84
Answer: C. 72
Explanation: Pattern is n² + n.
1² + 1 = 2
2² + 4 = 8
6² + 6 = 72
28. 6, 24, 60, 120, ?
A. 180
B. 200
C. 210
D. 240
Answer: C. 210
Explanation: Pattern is n³ − n.
2³ − 2 = 6
3³ − 3 = 24
6³ − 6 = 210
29. 3, 7, 15, 31, 63, ?
A. 95
B. 111
C. 127
D. 135
Answer: C. 127
Explanation: Multiply by 2 and add 1.
3 × 2 + 1 = 7
7 × 2 + 1 = 15
63 × 2 + 1 = 127
30. 1, 2, 3, 5, 8, ?
A. 11
B. 12
C. 13
D. 14
Answer: C. 13
Explanation: Fibonacci series.
1 + 2 = 3
2 + 3 = 5
5 + 8 = 13
31. 4, 8, 12, 16, 20, ?
A. 22
B. 24
C. 26
D. 28
Answer: B. 24
Explanation: Add 4 each time.
20 + 4 = 24
32. 60, 54, 48, 42, 36, ?
A. 28
B. 30
C. 32
D. 34
Answer: B. 30
Explanation: Subtract 6 each time.
36 − 6 = 30
33. 6, 12, 24, 48, 96, ?
A. 144
B. 168
C. 192
D. 200
Answer: C. 192
Explanation: Multiply by 2 each time.
96 × 2 = 192
34. 243, 81, 27, 9, ?
A. 1
B. 2
C. 3
D. 6
Answer: C. 3
Explanation: Divide by 3 each time.
9 ÷ 3 = 3
35. 16, 25, 36, 49, 64, ?
A. 72
B. 81
C. 100
D. 121
Answer: B. 81
Explanation: Perfect squares.
4² = 16
5² = 25
9² = 81
36. 64, 125, 216, 343, ?
A. 512
B. 625
C. 729
D. 1000
Answer: A. 512
Explanation: Perfect cubes.
4³ = 64
5³ = 125
8³ = 512
37. 2, 6, 12, 20, 30, ?
A. 40
B. 42
C. 44
D. 46
Answer: B. 42
Explanation: Pattern is n² + n.
6² + 6 = 42
38. 0, 6, 24, 60, 120, ?
A. 180
B. 190
C. 200
D. 210
Answer: D. 210
Explanation: Pattern is n³ − n.
6³ − 6 = 210
39. 4, 9, 19, 39, 79, ?
A. 119
B. 139
C. 159
D. 199
Answer: C. 159
Explanation: Multiply by 2 and add 1.
79 × 2 + 1 = 159
40. 5, 8, 13, 21, 34, ?
A. 45
B. 50
C. 55
D. 55
Answer: D. 55
Explanation: Fibonacci series.
5 + 8 = 13
8 + 13 = 21
21 + 34 = 55
41. 6, 11, 16, 21, 26, ?
A. 29
B. 30
C. 31
D. 32
Answer: C. 31
Explanation: Add 5 each time.
26 + 5 = 31
42. 90, 82, 74, 66, 58, ?
A. 48
B. 50
C. 52
D. 54
Answer: B. 50
Explanation: Subtract 8 each time.
58 − 8 = 50
43. 7, 14, 28, 56, 112, ?
A. 168
B. 196
C. 224
D. 256
Answer: C. 224
Explanation: Multiply by 2 each time.
112 × 2 = 224
44. 729, 243, 81, 27, 9, ?
A. 1
B. 2
C. 3
D. 6
Answer: C. 3
Explanation: Divide by 3 each time.
9 ÷ 3 = 3
45. 25, 36, 49, 64, 81, ?
A. 90
B. 99
C. 100
D. 121
Answer: C. 100
Explanation: Perfect squares.
5² = 25
6² = 36
10² = 100
46. 125, 216, 343, 512, ?
A. 625
B. 729
C. 1000
D. 1331
Answer: B. 729
Explanation: Perfect cubes.
5³ = 125
6³ = 216
9³ = 729
47. 2, 6, 12, 20, 30, ?
A. 40
B. 41
C. 42
D. 43
Answer: C. 42
Explanation: Pattern is n² + n.
6² + 6 = 42
48. 0, 6, 24, 60, 120, ?
A. 180
B. 190
C. 200
D. 210
Answer: D. 210
Explanation: Pattern is n³ − n.
6³ − 6 = 210
49. 5, 11, 23, 47, 95, ?
A. 181
B. 189
C. 191
D. 193
Answer: C. 191
Explanation: Multiply by 2 and add 1.
95 × 2 + 1 = 191
50. 8, 13, 21, 34, 55, ?
A. 76
B. 81
C. 89
D. 94
Answer: C. 89
Explanation: Fibonacci series.
21 + 34 = 55
34 + 55 = 89
Conclusion
We learned important concepts and Number Series Tricks used in reasoning questions for competitive exams. We covered addition, subtraction, multiplication, division, squares, cubes, Fibonacci series, step differences, mixed patterns, alternative series, and many other important logics. To become strong in number series, revise all patterns regularly and practice different types of questions every day. The more series you solve, the faster you can identify hidden patterns in exams.
Always try to find new logic and different ways to solve a series instead of depending on only one method. Sometimes a question may look difficult, but checking differences, square numbers, cubes, or alternate patterns can make it easy. In competitive exams like SSC, Banking, Railways, UPSC, Police, and other government exams, Number Series Tricks help improve speed, accuracy, and confidence. With proper practice and smart observation, you can solve number-series questions quickly and score better in the reasoning section.
FAQs
Q1. What is a number series in reasoning?
A: A number series is a sequence of numbers that follows a hidden pattern or logic.
Q2. Why are Number Series Tricks important?
A: Number Series Tricks help solve reasoning questions faster and improve accuracy in competitive exams.
Q3. Which exams ask number series questions?
A: Number series questions are common in SSC, Banking, Railways, UPSC, Police, Defence, and other government exams.
Q4. What should I check first in a number series?
A: First check addition, subtraction, multiplication, division, and step differences.
Q5. How can I improve in number series?
A: Practice daily, revise important patterns, and learn different logic methods regularly.
