NUMBER SERIES –
1\. Introduction to Number Series
A Number Series is an important topic in the Reasoning Ability section of competitive examinations. It consists of a sequence of numbers arranged according to a particular mathematical rule or pattern.
Candidates are required to identify the relationship between the numbers and find the missing number, next number or incorrect number in the given series.
Example 1:
2, 4, 6, 8, 10, ?
Solution:
The difference between consecutive numbers is 2.
2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
8 + 2 = 10
10 + 2 = 12
Answer: 12
Example 2:
3, 6, 12, 24, 48, ?
Solution:
Each number is multiplied by 2.
3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
24 × 2 = 48
48 × 2 = 96
Answer: 96
### Importance of Number Series
Number Series questions test the following abilities:
* Logical and analytical reasoning.
* Identification of mathematical patterns.
* Calculation speed and accuracy.
* Observation and problem-solving skills.
* Understanding of number relationships.
* Application of basic mathematical operations.
### 2\. Types of Number Series
Number Series questions can be classified into the following major types:
* Addition Series
* Subtraction Series
* Multiplication Series
* Division Series
* Square Number Series
* Cube Number Series
* Prime Number Series
* Difference Series
* Alternate Number Series
* Mixed Operation Series
* Fibonacci Series
* Missing Number Series
* Wrong Number Series
* Fractional Number Series
* Decimal Number Series
* Increasing and Decreasing Difference Series
* Pattern-Based Number Series
* Combination Series
Let us study each type with rules, examples and explanations.
### 3\. Addition Number Series
In this type of series, a fixed number or an increasing/decreasing number is added to the previous term to obtain the next term.
Example 1:
5, 10, 15, 20, 25, ?
Solution:
5 + 5 = 10
10 + 5 = 15
15 + 5 = 20
20 + 5 = 25
25 + 5 = 30
Answer: 30
Example 2:
3, 7, 12, 18, 25, ?
Solution:
Find the differences:
7 − 3 = 4
12 − 7 = 5
18 − 12 = 6
25 − 18 = 7
The differences are 4, 5, 6, 7.
The next difference will be 8.
25 + 8 = 33.
Answer: 33
Example 3:
2, 5, 9, 14, 20, 27, ?
Differences:
+3, +4, +5, +6, +7
Next difference = +8.
27 + 8 = 35.
Answer: 35
### 4\. Subtraction Number Series
In this type, a particular number is subtracted from the previous number to obtain the next number.
Example 1:
100, 90, 80, 70, 60, ?
Solution:
100 − 10 = 90
90 − 10 = 80
80 − 10 = 70
70 − 10 = 60
60 − 10 = 50
Answer: 50
Example 2:
90, 85, 77, 66, 52, ?
Solution:
Differences:
−5, −8, −11, −14
The difference increases by 3.
Next difference = −17.
52 − 17 = 35.
Answer: 35
### 5\. Multiplication Number Series
In this type, each number is multiplied by a fixed number or by an increasing or decreasing multiplier.
Example 1:
2, 4, 8, 16, 32, ?
Solution:
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
32 × 2 = 64
Answer: 64
Example 2:
3, 6, 18, 72, 360, ?
Solution:
3 × 2 = 6
6 × 3 = 18
18 × 4 = 72
72 × 5 = 360
360 × 6 = 2160
Answer: 2160
Example 3:
2, 6, 24, 120, 720, ?
Multipliers:
×3, ×4, ×5, ×6
Next multiplier = ×7.
720 × 7 = 5040.
Answer: 5040
### 6\. Division Number Series
In this type, each number is divided by a particular number to obtain the next term.
Example 1:
640, 320, 160, 80, 40, ?
Solution:
640 ÷ 2 = 320
320 ÷ 2 = 160
160 ÷ 2 = 80
80 ÷ 2 = 40
40 ÷ 2 = 20
Answer: 20
Example 2:
729, 243, 81, 27, 9, ?
Each number is divided by 3.
9 ÷ 3 = 3.
Answer: 3
### 7\. Square Number Series
Square numbers are obtained by multiplying a natural number by itself.
Formula:
n^2=n\\times n
### Important Square Numbers
| Number | Square |
| ------ | ------ |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
| 17 | 289 |
| 18 | 324 |
| 19 | 361 |
| 20 | 400 |
Example 1:
1, 4, 9, 16, 25, 36, ?
These are squares:
1², 2², 3², 4², 5², 6².
Next number = 7² = 49.
Answer: 49
Example 2:
4, 9, 16, 25, 36, ?
These are squares of 2, 3, 4, 5 and 6.
Next number = 7² = 49.
Answer: 49
Example 3:
2, 5, 10, 17, 26, ?
Observe:
1² + 1 = 2
2² + 1 = 5
3² + 1 = 10
4² + 1 = 17
5² + 1 = 26
Next = 6² + 1 = 37.
Answer: 37
### 8\. Cube Number Series
Cube numbers are obtained by multiplying a number three times by itself.
Formula:
n^3=n\\times n\\times n
### Important Cube Numbers
| Number | Cube |
| ------ | ---- |
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1000 |
| 11 | 1331 |
| 12 | 1728 |
| 13 | 2197 |
| 14 | 2744 |
| 15 | 3375 |
Example 1:
1, 8, 27, 64, 125, ?
These are cubes:
1³, 2³, 3³, 4³, 5³.
Next = 6³ = 216.
Answer: 216
Example 2:
8, 27, 64, 125, 216, ?
These are cubes of 2, 3, 4, 5 and 6.
Next = 7³ = 343.
Answer: 343
Example 3:
9, 28, 65, 126, 217, ?
Observe:
2³ + 1 = 9
3³ + 1 = 28
4³ + 1 = 65
5³ + 1 = 126
6³ + 1 = 217
Next = 7³ + 1 = 344.
Answer: 344
### 9\. Prime Number Series
A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.
### Important Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Important Facts:
* 2 is the smallest prime number.
* 2 is the only even prime number.
* 1 is neither prime nor composite.
* Every prime number greater than 2 is odd.
* 9, 15, 21 and 25 are composite numbers.
Example 1:
2, 3, 5, 7, 11, 13, ?
These are consecutive prime numbers.
Next prime number = 17.
Answer: 17
Example 2:
5, 10, 15, 21, 28, 36, ?
Differences:
+5, +5, +6, +7, +8.
This series does not follow a simple prime-number pattern. Always check the actual differences before identifying a rule.
### 10\. Difference Number Series
In this type, the differences between consecutive numbers follow a particular pattern.
Example 1:
2, 5, 10, 17, 26, 37, ?
Differences:
+3, +5, +7, +9, +11.
Next difference = +13.
37 + 13 = 50.
Answer: 50
Example 2:
1, 4, 9, 16, 25, 36, ?
Differences:
+3, +5, +7, +9, +11.
Next difference = +13.
36 + 13 = 49.
Answer: 49
Example 3:
3, 8, 15, 24, 35, 48, ?
Differences:
+5, +7, +9, +11, +13.
Next difference = +15.
48 + 15 = 63.
Answer: 63
### 11\. Alternate Number Series
In an alternate number series, two different patterns operate simultaneously. The terms in odd positions and even positions follow separate mathematical rules.
Example 1:
2, 5, 4, 10, 6, 15, 8, ?
Solution:
Separate the odd-position and even-position numbers.
Odd positions: 2, 4, 6, 8
Pattern: +2
Even positions: 5, 10, 15, ?
Pattern: +5
Next even-position number = 20.
Answer: 20
Example 2:
3, 10, 5, 20, 7, 30, 9, ?
Odd positions: 3, 5, 7, 9
Even positions: 10, 20, 30, ?
Next number = 40.
Answer: 40
Example 3:
2, 8, 4, 16, 6, 32, 8, ?
Odd positions: 2, 4, 6, 8
Even positions: 8, 16, 32, ?
Even-position pattern: ×2.
Next number = 64.
Answer: 64
Exam Tip: Whenever a series does not show an obvious relationship between consecutive numbers, separate the odd and even positions.
### 12\. Fibonacci Number Series
The Fibonacci series is a sequence in which each number is obtained by adding the previous two numbers.
General Rule:
Next term = Previous term + Second previous term.
Example 1:
0, 1, 1, 2, 3, 5, 8, 13, ?
Solution:
0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
Answer: 21
Example 2:
2, 3, 5, 8, 13, 21, ?
Solution:
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
Answer: 34
Example 3:
4, 7, 11, 18, 29, 47, ?
Solution:
4 + 7 = 11
7 + 11 = 18
11 + 18 = 29
18 + 29 = 47
29 + 47 = 76
Answer: 76
### 13\. Mixed Operation Number Series
In this type of series, more than one mathematical operation is used, such as addition, multiplication, subtraction and division.
Example 1:
2, 5, 11, 23, 47, ?
Solution:
2 × 2 + 1 = 5
5 × 2 + 1 = 11
11 × 2 + 1 = 23
23 × 2 + 1 = 47
47 × 2 + 1 = 95
Answer: 95
Example 2:
3, 8, 18, 38, 78, ?
Rule:
3 × 2 + 2 = 8
8 × 2 + 2 = 18
18 × 2 + 2 = 38
38 × 2 + 2 = 78
78 × 2 + 2 = 158
Answer: 158
Example 3:
5, 11, 23, 47, 95, ?
Rule: Multiply by 2 and add 1.
95 × 2 + 1 = 191.
Answer: 191
### 14\. Increasing Difference Number Series
In this type, the difference between consecutive terms increases according to a particular pattern.
Example 1:
1, 3, 7, 13, 21, 31, ?
Differences:
+2, +4, +6, +8, +10.
Next difference = +12.
31 + 12 = 43.
Answer: 43
Example 2:
2, 6, 12, 20, 30, 42, ?
Differences:
+4, +6, +8, +10, +12.
Next difference = +14.
42 + 14 = 56.
Answer: 56
Example 3:
10, 15, 23, 34, 48, 65, ?
Differences:
+5, +8, +11, +14, +17.
Next difference = +20.
65 + 20 = 85.
Answer: 85
### 15\. Decreasing Difference Number Series
In this type, the differences between consecutive terms decrease according to a particular pattern.
Example 1:
100, 90, 82, 76, 72, 70, ?
Differences:
−10, −8, −6, −4, −2.
Next difference = 0.
70 − 0 = 70.
Answer: 70
Example 2:
200, 180, 165, 155, 150, ?
Differences:
−20, −15, −10, −5.
Next difference = 0.
150 − 0 = 150.
Answer: 150
### 16\. Square-Based Number Series
Some number series are formed by adding, subtracting or multiplying square numbers.
Example 1:
2, 5, 10, 17, 26, ?
Rule:
1² + 1 = 2
2² + 1 = 5
3² + 1 = 10
4² + 1 = 17
5² + 1 = 26
6² + 1 = 37
Answer: 37
Example 2:
3, 8, 15, 24, 35, ?
Rule:
2² − 1 = 3
3² − 1 = 8
4² − 1 = 15
5² − 1 = 24
6² − 1 = 35
7² − 1 = 48
Answer: 48
Example 3:
5, 10, 17, 26, 37, ?
Rule:
2² + 1 = 5
3² + 1 = 10
4² + 1 = 17
5² + 1 = 26
6² + 1 = 37
7² + 1 = 50
Answer: 50
### 17\. Cube-Based Number Series
These series are formed using cube numbers or combinations of cubes.
Example 1:
2, 9, 28, 65, 126, ?
Rule:
1³ + 1 = 2
2³ + 1 = 9
3³ + 1 = 28
4³ + 1 = 65
5³ + 1 = 126
6³ + 1 = 217
Answer: 217
Example 2:
7, 26, 63, 124, 215, ?
Rule:
2³ − 1 = 7
3³ − 1 = 26
4³ − 1 = 63
5³ − 1 = 124
6³ − 1 = 215
7³ − 1 = 342
Answer: 342
### 18\. Fractional Number Series
In this type, numbers are represented in fractional form. The numerator, denominator or both may follow a particular pattern.
Example 1:
1/2, 2/3, 3/4, 4/5, 5/6, ?
Solution:
Numerators: 1, 2, 3, 4, 5.
Denominators: 2, 3, 4, 5, 6.
Next fraction = 6/7.
Answer: 6/7
Example 2:
1/3, 2/6, 3/9, 4/12, ?
Numerators increase by 1.
Denominators increase by 3.
Next fraction = 5/15.
Answer: 5/15
### 19\. Decimal Number Series
Decimal series contain numbers with decimal points. Their patterns may involve addition, subtraction, multiplication or division.
Example 1:
0.5, 1.0, 1.5, 2.0, 2.5, ?
Difference = 0.5.
Next number = 3.0.
Answer: 3.0
Example 2:
0.2, 0.4, 0.8, 1.6, 3.2, ?
Each number is multiplied by 2.
3.2 × 2 = 6.4.
Answer: 6.4
### 20\. Missing Number Series
In missing number questions, one or more terms are missing from a given sequence. Candidates must identify the mathematical pattern and find the missing values.
Example 1:
5, 10, ?, 20, 25, 30.
Solution:
The series increases by 5.
5, 10, 15, 20, 25, 30.
Answer: 15
Example 2:
3, 9, 27, ?, 243.
Solution:
Each term is multiplied by 3.
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
81 × 3 = 243
Answer: 81
Example 3:
4, 9, 16, ?, 36, 49.
These are squares:
2², 3², 4², 5², 6², 7².
Answer: 25
Example 4:
2, 6, 12, ?, 30, 42.
Differences:
+4, +6, +8, +10, +12.
Missing number = 12 + 8 = 20.
Answer: 20
### 21\. Wrong Number Series
In this type, one number in the sequence does not follow the established mathematical pattern. Candidates must identify the incorrect number.
Example 1:
2, 4, 8, 16, 31, 64.
Solution:
The pattern is multiplication by 2.
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
32 × 2 = 64
Therefore, 31 is incorrect.
Answer: 31
Example 2:
1, 4, 9, 16, 24, 36, 49.
Solution:
These are consecutive square numbers:
1², 2², 3², 4², 5², 6², 7².
The correct fifth term is 25, not 24.
Answer: 24
Example 3:
3, 6, 12, 24, 48, 90.
Each term should be multiplied by 2.
48 × 2 = 96.
Therefore, 90 is incorrect.
Answer: 90
### 22\. Prime Number-Based Series
Some series use prime numbers in combination with other mathematical operations.
Example 1:
3, 5, 9, 15, 23, ?
Differences:
+2, +4, +6, +8.
Next difference = +10.
23 + 10 = 33.
Answer: 33
Example 2:
2, 6, 12, 20, 30, ?
Rule: Consecutive natural numbers multiplied by their successors.
1 × 2 = 2
2 × 3 = 6
3 × 4 = 12
4 × 5 = 20
5 × 6 = 30
6 × 7 = 42.
Answer: 42
### 23\. Important Mathematical Patterns for Number Series
Candidates should memorise the following patterns because they are frequently useful in solving number series questions.
### A. Natural Numbers
1, 2, 3, 4, 5, 6, 7, 8, 9, 10...
### B. Even Numbers
2, 4, 6, 8, 10, 12, 14, 16, 18, 20...
### C. Odd Numbers
1, 3, 5, 7, 9, 11, 13, 15, 17, 19...
### D. Consecutive Square Numbers
1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
### E. Consecutive Cube Numbers
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000...
### F. Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
### G. Triangular Numbers
1, 3, 6, 10, 15, 21, 28, 36, 45, 55...
Formula:
T_n=\\frac{n(n+1)}{2}
### H. Powers of 2
1, 2, 4, 8, 16, 32, 64, 128, 256, 512...
### I. Powers of 3
1, 3, 9, 27, 81, 243, 729...
### J. Powers of 10
1, 10, 100, 1000, 10000...
### K. Factorial Numbers
1, 2, 6, 24, 120, 720, 5040...
Explanation:
1! = 1
2! = 1 × 2 = 2
3! = 1 × 2 × 3 = 6
4! = 1 × 2 × 3 × 4 = 24
5! = 1 × 2 × 3 × 4 × 5 = 120
### L. Fibonacci Numbers
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
### 24\. Advanced Number Series Patterns
These patterns are useful for solving moderate and difficult questions in banking, SSC, JKSSB and other competitive examinations.
### A. Multiplication with Increasing Addition
Example:
2, 5, 12, 27, 58, ?
Pattern:
2 × 2 + 1 = 5
5 × 2 + 2 = 12
12 × 2 + 3 = 27
27 × 2 + 4 = 58
58 × 2 + 5 = 121
Answer: 121
### B. Multiplication with Decreasing Subtraction
Example:
100, 49, 24, 11, 4, ?
Pattern:
100 ÷ 2 − 1 = 49
49 ÷ 2 − 0.5 = 24 (this does not continue as a simple integer rule).
Instead, examine the differences:
−51, −25, −13, −7.
The differences approximately halve, with rounding. Such a sequence should not be accepted without a consistent exact rule. In an examination, always verify every term.
### C. Increasing Multiplication
Example:
2, 4, 12, 48, 240, ?
Multipliers:
×2, ×3, ×4, ×5.
Next multiplier = ×6.
240 × 6 = 1440.
Answer: 1440
### D. Decreasing Multiplication or Division
Example:
720, 120, 24, 6, 2, ?
Divisors:
÷6, ÷5, ÷4, ÷3.
Next divisor = 2.
2 ÷ 2 = 1.
Answer: 1
### E. Alternating Mathematical Operations
Example:
3, 6, 8, 16, 18, 36, ?
Pattern:
3 × 2 = 6
6 + 2 = 8
8 × 2 = 16
16 + 2 = 18
18 × 2 = 36
36 + 2 = 38
Answer: 38
### F. Powers of Numbers
Example:
1, 4, 27, 256, 3125, ?
Pattern:
1¹ = 1
2² = 4
3³ = 27
4⁴ = 256
5⁵ = 3125
6⁶ = 46656.
Answer: 46656
### G. Product of Consecutive Numbers
Example:
6, 12, 20, 30, 42, ?
Pattern:
2 × 3 = 6
3 × 4 = 12
4 × 5 = 20
5 × 6 = 30
6 × 7 = 42
7 × 8 = 56
Answer: 56
### H. Combination of Square and Cube Numbers
Example:
2, 9, 28, 65, 126, ?
Pattern:
1³ + 1 = 2
2³ + 1 = 9
3³ + 1 = 28
4³ + 1 = 65
5³ + 1 = 126
6³ + 1 = 217
Answer: 217
### 25\. Difference of Differences Method
This is one of the most useful techniques for solving difficult number series.
When the differences between consecutive terms are not constant, calculate the differences again.
Example 1:
2, 5, 11, 20, 32, ?
First differences:
5 − 2 = 3
11 − 5 = 6
20 − 11 = 9
32 − 20 = 12
First difference series:
3, 6, 9, 12.
Second differences:
+3, +3, +3.
Next first difference = 15.
32 + 15 = 47.
Answer: 47
Example 2:
1, 8, 27, 64, 125, ?
These are cube numbers.
Another way to observe:
First differences:
7, 19, 37, 61.
Second differences:
12, 18, 24.
Third differences:
6, 6.
The constant third difference confirms a cubic pattern.
Next number = 216.
Answer: 216
Example 3:
1, 2, 6, 15, 31, 56, ?
First differences:
1, 4, 9, 16, 25.
These are consecutive square numbers.
Next difference = 36.
56 + 36 = 92.
Answer: 92
### 26\. Special Number Series Based on Triangular Numbers
Triangular numbers are formed by adding consecutive natural numbers.
Sequence:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55...
Formula:
T_n=\\frac{n(n+1)}{2}
Example 1:
3, 6, 10, 15, 21, ?
Differences:
+3, +4, +5, +6.
Next difference = +7.
21 + 7 = 28.
Answer: 28
Example 2:
1, 3, 6, 10, 15, 21, ?
Next triangular number = 28.
Answer: 28
### 27\. How to Solve Number Series Questions Quickly
A systematic approach helps candidates identify the correct pattern without wasting time.
### Step 1: Check the Difference
Subtract each number from the next number.
Example:
4, 9, 14, 19, 24, ?
Differences = +5, +5, +5, +5.
Answer = 29.
### Step 2: Check Multiplication and Division
Example:
5, 10, 20, 40, 80, ?
Each number is multiplied by 2.
Answer = 160.
### Step 3: Check Square Numbers
Example:
9, 16, 25, 36, 49, ?
These are squares of 3, 4, 5, 6 and 7.
Answer = 64.
### Step 4: Check Cube Numbers
Example:
27, 64, 125, 216, ?
These are cubes of 3, 4, 5 and 6.
Answer = 343.
### Step 5: Check Alternate Terms
Example:
2, 10, 4, 20, 6, 30, ?
Odd-position terms: 2, 4, 6.
Even-position terms: 10, 20, 30.
Next odd-position term = 8.
Answer: 8
### Step 6: Check Prime Numbers
Example:
2, 3, 5, 7, 11, 13, ?
Next prime number = 17.
### Step 7: Check Mixed Operations
Example:
4, 9, 19, 39, 79, ?
Pattern: ×2 + 1.
79 × 2 + 1 = 159.
Answer: 159
### Step 8: Check the Difference of Differences
If the first difference does not show a clear pattern, calculate the second and possibly the third differences.
This technique is particularly useful for square-based, cube-based and polynomial series.
### 28\. Important Shortcuts and Tricks
| Pattern | Shortcut |
| ----------------------- | -------------------------------------------- |
| Constant difference | Subtract consecutive terms |
| Constant multiplication | Divide consecutive terms |
| Square series | Check n² |
| Cube series | Check n³ |
| Prime series | Check prime numbers |
| Fibonacci series | Add previous two terms |
| Alternate series | Separate odd and even positions |
| Increasing differences | Check the difference sequence |
| Decreasing series | Check subtraction and division |
| Factorial series | Check multiplication by consecutive integers |
| Mixed operations | Check ×2 ± 1, ×3 ± 1, etc. |
| Wrong number | Verify each term against the same rule |
### Quick Revision: What to Check First
* Difference between consecutive terms.
* Multiplication or division.
* Increasing or decreasing differences.
* Square and cube numbers.
* Prime and factorial numbers.
* Alternate positions.
* Fibonacci pattern.
* Mixed mathematical operations.
This checking order is a practical approach to pattern recognition, not a guarantee that every question follows the same sequence of tests. SSC Education +2
### 29\. Common Mistakes Made by Candidates
* Applying a mathematical rule after checking only two terms.
* Ignoring alternate number patterns.
* Confusing squares with cubes.
* Making calculation errors while finding differences.
* Ignoring multiplication and division patterns.
* Spending too much time on a single question.
* Selecting an answer without verifying the complete sequence.
* Ignoring the possibility of a wrong number in the middle.
* Forgetting basic prime numbers, squares and cubes.
* Using an unnecessarily complicated rule when a simple rule explains all terms.
Important Advice: Always verify the proposed pattern against all the given terms before selecting an answer.
### 30\. Number Series Formula Revision
| Mathematical concept | Formula |
| ------------------------------ | ------- |
| Arithmetic progression | |
| Geometric progression | |
| Square number | |
| Cube number | |
| Triangular number | |
| Consecutive product | |
| Factorial | |
| Fibonacci series | |
| Sum of first n natural numbers | |
| Sum of first n squares | |
| Sum of first n cubes | |
### 31\. Practice Questions – Number Series MCQs
The following questions are designed for competitive examination preparation. Try to solve them independently before checking the answer key.
### Section A: Easy Level
Q1. 2, 4, 6, 8, 10, ?
(A) 11 (B) 12 (C) 14 (D) 16
Q2. 5, 10, 15, 20, 25, ?
(A) 28 (B) 30 (C) 35 (D) 40
Q3. 3, 6, 12, 24, 48, ?
(A) 72 (B) 84 (C) 96 (D) 108
Q4. 1, 4, 9, 16, 25, ?
(A) 30 (B) 36 (C) 40 (D) 49
Q5. 1, 8, 27, 64, 125, ?
(A) 196 (B) 200 (C) 216 (D) 225
Q6. 2, 3, 5, 7, 11, 13, ?
(A) 15 (B) 17 (C) 19 (D) 21
Q7. 100, 90, 80, 70, 60, ?
(A) 40 (B) 45 (C) 50 (D) 55
Q8. 2, 5, 10, 17, 26, ?
(A) 35 (B) 36 (C) 37 (D) 38
Q9. 3, 6, 18, 72, 360, ?
(A) 1800 (B) 2160 (C) 2520 (D) 2880
Q10. 1, 2, 3, 5, 8, 13, ?
(A) 18 (B) 20 (C) 21 (D) 24
### Section B: Moderate Level
Q11. 4, 9, 16, 25, 36, ?
(A) 42 (B) 45 (C) 49 (D) 64
Q12. 2, 6, 12, 20, 30, ?
(A) 36 (B) 40 (C) 42 (D) 48
Q13. 3, 8, 15, 24, 35, ?
(A) 46 (B) 48 (C) 50 (D) 52
Q14. 5, 11, 23, 47, 95, ?
(A) 181 (B) 189 (C) 191 (D) 195
Q15. 10, 15, 23, 34, 48, ?
(A) 62 (B) 65 (C) 66 (D) 68
Q16. 729, 243, 81, 27, 9, ?
(A) 1 (B) 2 (C) 3 (D) 6
Q17. 2, 5, 4, 10, 6, 15, 8, ?
(A) 16 (B) 18 (C) 20 (D) 24
Q18. 3, 10, 5, 20, 7, 30, 9, ?
(A) 35 (B) 36 (C) 40 (D) 45
Q19. 2, 4, 12, 48, 240, ?
(A) 1200 (B) 1240 (C) 1440 (D) 1480
Q20. 1, 3, 6, 10, 15, 21, ?
(A) 25 (B) 27 (C) 28 (D) 30
### Section C: Difficult Level
Q21. 2, 5, 11, 20, 32, ?
(A) 42 (B) 45 (C) 47 (D) 49
Q22. 3, 7, 15, 31, 63, ?
(A) 125 (B) 126 (C) 127 (D) 129
Q23. 4, 7, 13, 25, 49, ?
(A) 95 (B) 96 (C) 97 (D) 99
Q24. 1, 2, 6, 24, 120, ?
(A) 600 (B) 620 (C) 720 (D) 840
Q25. 2, 9, 28, 65, 126, ?
(A) 215 (B) 216 (C) 217 (D) 218
Q26. 2, 3, 5, 8, 13, 21, ?
(A) 32 (B) 33 (C) 34 (D) 35
Q27. 100, 90, 82, 76, 72, 70, ?
(A) 68 (B) 69 (C) 70 (D) 71
Q28. 5, 10, 17, 26, 37, 50, ?
(A) 63 (B) 64 (C) 65 (D) 66
Q29. 720, 120, 24, 6, 2, ?
(A) 0 (B) 1 (C) 2 (D) 3
Q30. 1, 4, 27, 256, 3125, ?
(A) 46656 (B) 36000 (C) 50000 (D) 62500
### 32\. Answer Key with Explanations
Solutions to all 30 MCQs
| Question | Correct answer | Explanation |
| -------- | -------------- | -------------------------------- |
| 1 | B – 12 | Add 2 |
| 2 | B – 30 | Add 5 |
| 3 | C – 96 | Multiply by 2 |
| 4 | B – 36 | Squares of 1 to 6 |
| 5 | C – 216 | Cubes of 1 to 6 |
| 6 | B – 17 | Consecutive prime numbers |
| 7 | C – 50 | Subtract 10 |
| 8 | C – 37 | Add consecutive odd numbers |
| 9 | B – 2160 | Multiply by 2, 3, 4, 5, 6 |
| 10 | C – 21 | Add previous two terms |
| 11 | C – 49 | Squares of 2 to 7 |
| 12 | C – 42 | Consecutive products |
| 13 | B – 48 | Differences +5, +7, +9, +11, +13 |
| 14 | C – 191 | Multiply by 2 and add 1 |
| 15 | B – 65 | Differences increase by 3 |
| 16 | C – 3 | Divide by 3 |
| 17 | C – 20 | Alternate series |
| 18 | C – 40 | Two alternate series |
| 19 | C – 1440 | Multiply by 2, 3, 4, 5, 6 |
| 20 | C – 28 | Triangular numbers |
| 21 | C – 47 | Differences 3, 6, 9, 12, 15 |
| 22 | C – 127 | Multiply by 2 and add 1 |
| 23 | C – 97 | Differences double |
| 24 | C – 720 | Factorial series |
| 25 | C – 217 | Cubes plus 1 |
| 26 | C – 34 | Fibonacci pattern |
| 27 | C – 70 | Subtract 10, 8, 6, 4, 2, 0 |
| 28 | C – 65 | Squares plus 1 |
| 29 | B – 1 | Divide by 6, 5, 4, 3, 2 |
| 30 | A – 46656 | Powers: 1¹, 2², 3³, 4⁴, 5⁵, 6⁶ |
### 33\. Additional Practice: Find the Missing Number
* 7, 14, 28, 56, ?, 224
* 11, 22, 33, ?, 55, 66
* 6, 12, 20, 30, ?, 56
* 1, 5, 14, 30, 55, ?
* 121, 144, 169, 196, ?, 256
* 8, 27, 64, ?, 216, 343
* 2, 7, 17, 37, 77, ?
* 4, 16, 64, 256, ?
* 13, 18, 26, 37, 51, ?
* 1, 4, 10, 20, 35, ?
Answer Key:
* 112
* 44
* 42
* 91
* 225
* 125
* 157
* 1024
* 68
* 56
### 34\. Additional Practice: Find the Wrong Number
Identify the incorrect number in each series.
* 2, 4, 8, 16, 30, 64
* 1, 4, 9, 16, 26, 36, 49
* 3, 6, 12, 24, 48, 95
* 5, 10, 17, 26, 38, 50
* 8, 27, 64, 125, 216, 344
* 2, 6, 12, 20, 32, 42
* 3, 5, 7, 11, 13, 17, 20
* 1, 2, 6, 24, 100, 720
* 10, 20, 40, 80, 150, 320
* 4, 9, 16, 25, 35, 49
Answer Key:
* 30 (should be 32)
* 26 (should be 25)
* 95 (should be 96)
* 38 (should be 37)
* 344 (should be 343)
* 32 (should be 30)
* 20 (should be 19)
* 100 (should be 120)
* 150 (should be 160)
* 35 (should be 36)
### 35\. Preparation Strategy for Competitive Examinations
To master Number Series, candidates should follow a regular practice routine.
Daily Study Plan
| Activity | Suggested time |
| -------------------------- | -------------- |
| Revision of basic concepts | 10 minutes |
| Square and cube practice | 5 minutes |
| Easy-level MCQs | 10 minutes |
| Moderate-level MCQs | 15 minutes |
| Difficult-level MCQs | 15 minutes |
| Revision of mistakes | 5 minutes |
| Total | 60 minutes |
### Important Preparation Tips
* Memorise squares up to 30 and cubes up to 15.
* Learn prime numbers up to 100.
* Practise multiplication tables up to 25.
* Solve at least 20–30 questions daily.
* Practise missing and wrong number series separately.
* Learn to identify alternate patterns.
* Maintain a notebook of difficult questions.
* Practise with a stopwatch to improve speed.
* Revise incorrect answers regularly.
### 36\. Conclusion
Number Series is an important and scoring topic in the Reasoning and Quantitative Aptitude sections of competitive examinations. It tests candidates' numerical ability, observation, logical thinking and problem-solving skills.
A candidate who understands the different mathematical patterns, memorises important squares, cubes and prime numbers, and practises questions regularly can improve both speed and accuracy.
The most important key to success in Number Series is understanding the pattern rather than memorising answers.
Prepare regularly, practise systematically and improve your accuracy to achieve better results in competitive examinations.
