<\/p>\n
Number series questions are among the most common and scoring-friendly items on the Civil Service Exam. They test your ability to recognize patterns, apply numerical logic, and predict the next value based on mathematical relationships. While many examinees find this section intimidating, most number series follow predictable rules\u2014once you understand these patterns, the questions become much easier to solve.<\/p>\n
This guide provides a complete overview of the most frequently used number series patterns, step-by-step solving strategies, and sample problems that reflect the Civil Service Exam style. By the end of this guide, you will have the confidence to approach any sequence with clarity and accuracy.<\/p>\n
A number series is a set of numbers arranged in a specific order that follows a hidden rule or pattern. Your task is to identify the rule and determine the next number (or missing number) in the sequence.<\/p>\n
Common number series formats include:<\/p>\n
Increasing or decreasing sequences<\/p>\n<\/li>\n
Alternating patterns<\/p>\n<\/li>\n
Patterns involving arithmetic or geometric operations<\/p>\n<\/li>\n
Mixed operations<\/p>\n<\/li>\n
Square, cube, or power-based progressions<\/p>\n<\/li>\n
Fibonacci or additive patterns<\/p>\n<\/li>\n
Difference-based patterns<\/p>\n<\/li>\n<\/ul>\n
Understanding these categories allows you to quickly analyze and classify the series in front of you.<\/p>\n
The Civil Service Exam includes number series questions to evaluate:<\/p>\n
Numerical reasoning<\/p>\n<\/li>\n
Pattern recognition<\/p>\n<\/li>\n
Logical thinking<\/p>\n<\/li>\n
Attention to detail<\/p>\n<\/li>\n
Ability to analyze data quickly<\/p>\n<\/li>\n<\/ul>\n
These skills are essential for government work that involves interpreting information, solving problems, and making decisions under time pressure.<\/p>\n
Number series questions are typically 10\u201315 items, depending on the exam type, and can significantly boost your score if you know the common patterns.<\/p>\n
Before learning specific types of patterns, you must master a universal approach that applies to all number sequences.<\/p>\n
Subtract each term from the next. If the differences form a pattern (e.g., +2, +4, +6), you\u2019re likely dealing with an arithmetic or incremental series.<\/p>\n
If the numbers grow or shrink quickly, check for multiplication patterns (\u00d72, \u00d73, \u00d71.5, etc.).<\/p>\n
Some series use a combination (e.g., \u00d72 + 1).<\/p>\n
Not all sequences are linear. Some alternate between two or more rules.<\/p>\n
Look for sequences involving powers, like 2\u00b2, 3\u00b2, 4\u00b2, or 2\u00b3, 3\u00b3, 4\u00b3.<\/p>\n
A common pattern involves adding the previous two numbers.<\/p>\n
Check whether your assumed pattern works consistently across the entire sequence.<\/p>\n
Below are the patterns you must master, along with explanations and examples.<\/p>\n
An arithmetic series changes by adding or subtracting a constant number.<\/p>\n
Example:<\/strong> Another example:<\/strong> Arithmetic series are the simplest to solve and appear frequently in the exam.<\/p>\n A geometric series multiplies or divides by a constant ratio.<\/p>\n Example:<\/strong> Another example:<\/strong> These sequences grow or shrink rapidly, making them easy to spot.<\/p>\n Some sequences use a changing difference (e.g., +1, +2, +3 \u2026).<\/p>\n Example:<\/strong> Another variation: These are extremely common in Civil Service exams.<\/p>\n Some sequences combine two operations repeatedly.<\/p>\n Example:<\/strong> But a more exam-accurate example: Every second number follows the same rule.<\/p>\n Example:<\/strong> Another example: Odd terms: +2<\/p>\n<\/li>\n Even terms: \u00d72 Alternating patterns require careful observation.<\/p>\n These series use perfect squares or cubes.<\/p>\n 1, 4, 9, 16, 25, ___ 1, 8, 27, 64, 125, ___ 3, 12, 27, 48, 75, ___ Each number is the sum of the previous two.<\/p>\n Example:<\/strong> Variant: Fibonacci patterns appear occasionally.<\/p>\n Some sequences combine multiple patterns across terms.<\/p>\n Example:<\/strong> This type is common for trick questions.<\/p>\n In exam settings, speed matters. Use this checklist:<\/p>\n Check the difference between numbers<\/strong> (simple or incremental?).<\/p>\n<\/li>\n Check the ratio<\/strong> (multiplication or division?).<\/p>\n<\/li>\n Look for alternating behavior<\/strong> (is every other term inconsistent?).<\/p>\n<\/li>\n Check for patterns in differences<\/strong> (e.g., +2, +4, +6).<\/p>\n<\/li>\n Consider powers or roots<\/strong> (squares, cubes).<\/p>\n<\/li>\n Look for mixed operations<\/strong> (\u00d72 + 1).<\/p>\n<\/li>\n Check if it resembles Fibonacci<\/strong>.<\/p>\n<\/li>\n<\/ol>\n Once you classify the type, solving becomes straightforward.<\/p>\n Below are 20 practice questions with explanations.<\/p>\n 4, 8, 16, 32, ___<\/p>\n<\/li>\n 5, 12, 19, 26, ___<\/p>\n<\/li>\n 3, 6, 7, 14, 15, 30, ___<\/p>\n<\/li>\n 10, 7, 8, 5, 6, 3, ___<\/p>\n<\/li>\n 2, 3, 6, 18, 72, ___<\/p>\n<\/li>\n 1, 4, 9, 16, ___<\/p>\n<\/li>\n 11, 13, 17, 23, ___<\/p>\n<\/li>\n 100, 90, 81, 73, ___<\/p>\n<\/li>\n 7, 14, 28, 56, ___<\/p>\n<\/li>\n 4, 9, 19, 39, ___<\/p>\n<\/li>\n 20, 25, 35, 50, ___<\/p>\n<\/li>\n 2, 5, 10, 17, 26, ___<\/p>\n<\/li>\n 30, 20, 25, 15, 20, ___<\/p>\n<\/li>\n 1, 2, 3, 5, 8, 13, ___<\/p>\n<\/li>\n 3, 5, 10, 12, 24, 26, ___<\/p>\n<\/li>\n 90, 30, 10, 3.33, ___<\/p>\n<\/li>\n 8, 16, 24, 48, ___<\/p>\n<\/li>\n 15, 18, 24, 33, ___<\/p>\n<\/li>\n 6, 12, 21, 33, ___<\/p>\n<\/li>\n 4, 6, 9, 13, 18, ___<\/p>\n<\/li>\n<\/ol>\n 64<\/strong> (\u00d72)<\/p>\n<\/li>\n 33<\/strong> (+7)<\/p>\n<\/li>\n 31<\/strong> (\u00d72, +1 alternating)<\/p>\n<\/li>\n 4<\/strong> (\u20133, +1 repeating)<\/p>\n<\/li>\n 360<\/strong> (\u00d71.5, \u00d72, \u00d73, \u00d74\u2026)<\/p>\n<\/li>\n 25<\/strong> (square numbers)<\/p>\n<\/li>\n 31<\/strong> (add prime differences: +2, +4, +6, +8\u2026)<\/p>\n<\/li>\n 66<\/strong> (\u201310, \u20139, \u20138\u2026)<\/p>\n<\/li>\n 112<\/strong> (\u00d72)<\/p>\n<\/li>\n 79<\/strong> (+5, +10, +20, +40\u2026)<\/p>\n<\/li>\n 70<\/strong> (+5, +10, +15, +20\u2026)<\/p>\n<\/li>\n 37<\/strong> (incrementing differences +3, +5, +7, +9\u2026)<\/p>\n<\/li>\n 25<\/strong> (\u201310, +5 repeating)<\/p>\n<\/li>\n 21<\/strong> (Fibonacci)<\/p>\n<\/li>\n 52<\/strong> (\u00d72, +2 repeating)<\/p>\n<\/li>\n 1.11<\/strong> (\u00f73 repeatedly)<\/p>\n<\/li>\n 72<\/strong> (+8, +8, \u00d72, +24\u2026)<\/p>\n<\/li>\n 45<\/strong> (+3, +6, +9, +12\u2026)<\/p>\n<\/li>\n 48<\/strong> (+6, +9, +12, +15\u2026)<\/p>\n<\/li>\n 24<\/strong> (+2, +3, +4, +5, +6\u2026)<\/p>\n<\/li>\n<\/ol>\n Do not overthink\u2014patterns are usually simple.<\/p>\n<\/li>\n Check both differences and ratios.<\/p>\n<\/li>\n Write down small differences; they reveal the pattern quickly.<\/p>\n<\/li>\n Review common patterns regularly until you recognize them instantly.<\/p>\n<\/li>\n Practice under timed conditions to improve speed.<\/p>\n<\/li>\n<\/ul>\n With mastery of these concepts, number series questions become some of the easiest items in the Civil Service Exam.<\/p>\n Below are practice questions modeled on Civil Service Exam style. Choose the next number (?) in each series.<\/p>\n 4, 8, 12, 16, ?<\/p>\n<\/li>\n 3, 9, 27, 81, ?<\/p>\n<\/li>\n 10, 7, 4, 1, ?<\/p>\n<\/li>\n 5, 10, 20, 40, ?<\/p>\n<\/li>\n 2, 5, 11, 23, 47, ?<\/p>\n<\/li>\n 7, 14, 21, 28, ?<\/p>\n<\/li>\n 1, 4, 9, 16, 25, ?<\/p>\n<\/li>\n 100, 90, 81, 73, ?<\/p>\n<\/li>\n 2, 3, 5, 8, 12, 17, ?<\/p>\n<\/li>\n 15, 12, 18, 15, 21, 18, ?<\/p>\n<\/li>\n 6, 12, 24, 48, ?<\/p>\n<\/li>\n 5, 11, 23, 47, 95, ?<\/p>\n<\/li>\n 1, 2, 4, 7, 11, 16, ?<\/p>\n<\/li>\n 9, 16, 25, 36, 49, ?<\/p>\n<\/li>\n 80, 70, 63, 57, 52, ?<\/p>\n<\/li>\n 3, 6, 12, 24, 48, ?<\/p>\n<\/li>\n 4, 7, 13, 25, 49, ?<\/p>\n<\/li>\n 2, 6, 18, 54, ?<\/p>\n<\/li>\n 11, 13, 17, 23, 31, ?<\/p>\n<\/li>\n 5, 8, 14, 26, 50, ?<\/p>\n<\/li>\n 30, 20, 25, 15, 20, 10, ?<\/p>\n<\/li>\n 1, 1, 2, 3, 5, 8, ?<\/p>\n<\/li>\n 4, 10, 22, 46, 94, ?<\/p>\n<\/li>\n 7, 9, 13, 21, 37, ?<\/p>\n<\/li>\n 90, 30, 10, 3.33, ?<\/p>\n<\/li>\n<\/ol>\n 20<\/strong><\/p>\n Pattern: +4 each time<\/p>\n<\/li>\n 4, 8, 12, 16, 20<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 243<\/strong><\/p>\n Pattern: \u00d73<\/p>\n<\/li>\n 3, 9, 27, 81, 243<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n \u20132<\/strong><\/p>\n Pattern: \u20133 each time<\/p>\n<\/li>\n 10, 7, 4, 1, \u20132<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 80<\/strong><\/p>\n Pattern: \u00d72<\/p>\n<\/li>\n 5, 10, 20, 40, 80<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 95<\/strong><\/p>\n Differences: +3, +6, +12, +24 (each difference \u00d72)<\/p>\n<\/li>\n Next difference: 24 \u00d7 2 = 48 \u2192 47 + 48 = 95<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 35<\/strong><\/p>\n Pattern: +7<\/p>\n<\/li>\n 7, 14, 21, 28, 35<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 36<\/strong><\/p>\n Perfect squares: 1\u00b2, 2\u00b2, 3\u00b2, 4\u00b2, 5\u00b2, 6\u00b2<\/p>\n<\/li>\n Next: 6\u00b2 = 36<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 66<\/strong><\/p>\n Differences: \u201310, \u20139, \u20138 \u2192 decreasing by 1<\/p>\n<\/li>\n Next difference: \u20137 \u2192 73 \u2013 7 = 66<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 23<\/strong><\/p>\n Differences: +1, +2, +3, +4, +5 \u2026<\/p>\n<\/li>\n 2, 3, 5, 8, 12, 17, next +6 \u2192 17 + 6 = 23<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 24<\/strong><\/p>\n Two alternating series:<\/p>\n 15, 18, 21, 24 (odd positions: +3)<\/p>\n<\/li>\n 12, 15, 18 (even positions: +3)<\/p>\n<\/li>\n<\/ul>\n<\/li>\n Next term is odd position \u2192 21 + 3 = 24<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 96<\/strong><\/p>\n Pattern: \u00d72<\/p>\n<\/li>\n 6, 12, 24, 48, 96<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 191<\/strong><\/p>\n Differences: +6, +12, +24, +48 (doubling)<\/p>\n<\/li>\n Next: +96 \u2192 95 + 96 = 191<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 22<\/strong><\/p>\n Differences: +1, +2, +3, +4, +5 \u2026<\/p>\n<\/li>\n Next difference: +6 \u2192 16 + 6 = 22<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 64<\/strong><\/p>\n Squares: 3\u00b2, 4\u00b2, 5\u00b2, 6\u00b2, 7\u00b2, 8\u00b2<\/p>\n<\/li>\n Next: 8\u00b2 = 64<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 48<\/strong><\/p>\n Differences: \u201310, \u20137, \u20136, \u20135, \u2026<\/p>\n<\/li>\n Next difference: \u20134 \u2192 52 \u2013 4 = 48<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n 96<\/strong><\/p>\n Pattern: \u00d72<\/p>\n<\/li>\n 3, 6, 12, 24, 48,
2, 6, 10, 14, 18, ___
Pattern: +4
Answer: 22<\/strong><\/p>\n
50, 45, 40, 35, ___
Pattern: \u20135
Answer: 30<\/strong><\/p>\n
\nGeometric Series<\/h2>\n
3, 9, 27, 81, ___
Pattern: \u00d73
Answer: 243<\/strong><\/p>\n
64, 32, 16, 8, ___
Pattern: \u00f72
Answer: 4<\/strong><\/p>\n
\nIncremental or Variable-Difference Series<\/h2>\n
1, 3, 6, 10, 15, ___
Differences: +2, +3, +4, +5
Answer: Next difference is +6 \u2192 21<\/strong><\/p>\n
4, 7, 12, 19, 28, ___
Differences: +3, +5, +7, +9
Next difference: +11 \u2192 39<\/strong><\/p>\n
\nMixed Operations (Addition + Multiplication)<\/h2>\n
2, 5, 15, 45, ___
Pattern: \u00d73, then +?
Actually: \u00d73 \u2192 2\u00d73 = 6 but result is 5
So the pattern is: \u00d73 \u2013 1
Thus: 45 \u00d7 3 \u2013 1 = 134<\/strong><\/p>\n
3, 7, 15, 31, 63, ___
Pattern: \u00d72 + 1
Answer: 63 \u00d7 2 + 1 = 127<\/strong><\/p>\n
\nAlternating Patterns<\/h2>\n
10, 7, 9, 6, 8, 5, ___
Odd positions: \u20131
Even positions: \u20131
Answer: Next term = 7<\/strong><\/p>\n
2, 10, 4, 20, 6, 30, ___
Pattern:<\/p>\n\n
Answer: Even term next \u2192 30 \u00d7 2 = 60<\/strong><\/p>\n<\/li>\n<\/ul>\n
\nSquare and Cube Series (Power Patterns)<\/h2>\n
Square-based<\/h3>\n
Pattern: n\u00b2
Answer: 36<\/strong><\/p>\nCube-based<\/h3>\n
Pattern: n\u00b3
Answer: 216<\/strong><\/p>\nMixed square operations<\/h3>\n
Pattern: n\u00b2 + 3
(2\u00b2+3=7? Not fitting. Let\u2019s try difference)
Differences: 9, 15, 21, 27 \u2192 +6
Thus next difference +6 \u2192 75 + 33 = 108<\/strong><\/p>\n
\nFibonacci-Type Series<\/h2>\n
1, 1, 2, 3, 5, 8, ___
Answer: 5 + 8 = 13<\/strong><\/p>\n
2, 3, 5, 8, 13, ___
Answer: 8 + 13 = 21<\/strong><\/p>\n
\nComplex or Multi-Step Patterns<\/h2>\n
5, 10, 8, 16, 14, 28, ___
Observe:
5 \u2192 10 (\u00d72)
10 \u2192 8 (\u20132)
8 \u2192 16 (\u00d72)
16 \u2192 14 (\u20132)
Pattern: \u00d72, \u20132
Next term: 14 \u00d7 2 = 28<\/strong><\/p>\n
\nHow to Quickly Identify the Pattern<\/h2>\n
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\nSample Civil Service Exam-Style Questions<\/h2>\n
\nPractice Questions (No Answers Yet)<\/h2>\n
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\nAnswer Key and Explanations<\/h2>\n
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\nFinal Tips for the Number Series Section<\/h2>\n
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\nProblem Sets: Number Series Practice<\/h2>\n
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\nAnswer Key and Explanations<\/h2>\n
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