Number Series – Civil Service Exam – Civil Service Exam Help

Number Series - Civil Service Exam

Introduction to Number Series

Number series problems are a common component of the civil service exam’s numerical ability section. These questions test your ability to recognize patterns in sequences of numbers, which can include arithmetic, geometric, and other logical sequences. Mastering these problems improves critical thinking and pattern recognition skills.

Types of Number Series

Arithmetic Series: A sequence where each term increases or decreases by a constant value (common difference).
Example: 3, 6, 9, 12, … (common difference: + 3)
Geometric Series: A sequence where each term is multiplied or divided by a constant factor (common ratio).
Example: 2, 4, 8, 16, … (common ratio: × 2)
Mixed Patterns: Sequences that combine arithmetic, geometric, or other logical patterns, such as alternating additions and subtractions.
Example: 5, 10, 7, 14, 11, …
Special Patterns: Sequences involving squares, cubes, prime numbers, or other mathematical operations.
Example: 1, 4, 9, 16, 25, … (squares of consecutive numbers)

Step-by-Step Approach to Solving Number Series Problems

Identify the Pattern: Look for a relationship between the terms. Check for addition, subtraction, multiplication, division, or alternating patterns.
Apply the Pattern: Use the identified pattern to find the next term or the missing term in the series.
Double-Check the Sequence: Ensure the pattern works consistently for all terms given in the series.

Example Problems and Solutions

Example 1:
Problem: Find the next term in the series: 7, 14, 21, 28, …
Solution:

This is an arithmetic series with a common difference of +7.
Next term:
Answer: The next term is 35.

Example 2:
Problem: Find the missing term in the series: 3, 6, __, 24, 48.
Solution:

This is a geometric series with a common ratio of × 2.
Missing term:
Answer: The missing term is 12.

Common Mistakes to Avoid

Ignoring the pattern type: Always check for multiple types of patterns, as some series might not be straightforward.
Rushing through calculations: Take your time to apply the identified pattern correctly.
Missing alternating patterns: Some series switch operations, so double-check the sequence if something seems off.

Key Tips for the Exam

Familiarize yourself with different patterns by practicing various types of series.
Write down the differences or ratios between terms to help identify the pattern.
Practice with timed exercises to improve speed and accuracy.

Problem 1:

Series: 2, 4, 8, 16, 32, 64, ___

Choices:

A) 96

B) 100

C) 128

D) 132

Correct Answer: C) 128

Solution: This series is a simple progression where each number is doubled to get the next. Thus: $64 \times 2 = 128$

Problem 2:

Series: 1, 3, 7, 15, 31, 63, ___

Choices:

A) 127

B) 128

C) 129

D) 130

Correct Answer: A) 127

Solution: Each number in the series is obtained by doubling the previous number and adding 1.

Therefore: $63 \times 2 + 1 = 126 + 1 = 127$

Problem 3:

Series: 5, 10, 20, 40, 80, 160, ___

Choices:

A) 310

B) 320

C) 330

D) 340

Correct Answer: B) 320

Solution: The pattern shows each number is doubled to obtain the next number in the series. Thus: $160 \times 2 = 320$

Problem 4:

Series: 6, 12, 24, 48, 96, 192, ___

Choices:

A) 288

B) 384

C) 390

D) 400

Correct Answer: B) 384

Solution: Similar to the previous series, each number doubles the previous one. Following this rule: $192 \times 2 = 384$

Problem 5:

Series: 3, 6, 12, 24, 48, 96, ___

Choices:

A) 144

B) 192

C) 198

D) 200

Correct Answer: B) 192

Solution: Each number is the result of multiplying the previous number by 2. Applying this pattern:

Problem 6:

Series: 1, 4, 9, 16, 25, ___

Choices:

A) 30

B) 36

C) 42

D) 49

Correct Answer: B) 36

Solution: This series represents the squares of consecutive integers. Thus:

Problem 7:

Series: 2, 3, 5, 8, 12, 17, ___

Choices:

A) 21

B) 22

C) 23

D) 24

Correct Answer: C) 23

Solution: This series increments by successively increasing values: 1, 2, 3, 4, 5, etc. The pattern shows each next number is the sum of the current number and its incremental value: $17 + 6 = 23$

Problem 8:

Series: 10, 13, 17, 22, 28, ___

Choices:

A) 34

B) 35

C) 36

D) 37

Correct Answer: B) 35

Solution:

Number Series Exercises

1. Identify the next number in the series: 3, 9, 27, 81, …

2.What is the next number in the series: 4, 8, 16, 32, …

3. What is the next number in the series: 2, 6, 18, 54, …

4. Identify the next number in the series: 10, 13, 18, 25, 34, …

5. What is the next number in the series: 1, 1, 2, 3, 5, 8, …

6. Find the next number in the series: 5, 10, 20, 40, 80, …

7. Determine the next number in the series: 2, 3, 5, 8, 12, …

8. Question: What is the next number in the series: 0, 1, 1, 2, 4, 7, 13, …

9. What is the next number in the series: 40, 80, 60, 120, 100, 200, 180…

10. Identify the next number in the series: 30, 150, 100, 500, 450, 2250, 2200, …

Answers

1. 243

2. 64

3. 162

4. 45

5. 13

6. 160

7. 17

8. 24

9. 360

10. 11,000