# Number Series – Rules, Shortcuts and Fully Worked Examples
**Aptitude & Reasoning | Day 21 | 2 November 2026 | 4:00 PM IST | TNPSC Grp IV**
A number series is a sequence in which the numbers follow a rule. In exams, identify the rule and then find the next number, a missing number or an incorrect number.
## 1. Common Types 1. **Addition:** 5, 10, 15, 20... (add 5 each time). 2. **Subtraction:** 80, 72, 64, 56... (subtract 8). 3. **Multiplication:** 3, 6, 12, 24... (multiply by 2). 4. **Division:** 128, 64, 32, 16... (divide by 2). 5. **Squares:** 1, 4, 9, 16, 25... (1², 2², 3²...). 6. **Cubes:** 1, 8, 27, 64, 125... (1³, 2³...). 7. **Changing differences:** 2, 5, 10, 17, 26... (add 3, 5, 7, 9). 8. **Fibonacci:** 1, 1, 2, 3, 5, 8, 13... (sum of the previous two numbers). 9. **Alternating series:** Odd and even positions may follow different rules.
## 2. Fast Method **Step 1:** Subtract consecutive terms to check the differences. **Step 2:** If differences change, inspect their pattern. **Step 3:** Check multiplication, division, perfect squares and cubes. **Step 4:** Examine alternate positions separately. **Step 5:** Make sure the rule fits every given term. A short sequence may have several mathematical continuations; choose the simplest consistent exam-style rule.
## 3. Six Fully Worked Examples **Example 1 – Increasing differences:** 4, 7, 12, 19, 28, ? Differences are +3,+5,+7,+9. Next difference = +11. Therefore 28+11 = **39**. **Answer: 39.**
**Example 2 – Multiplication:** 5, 15, 45, 135, ? Each term is multiplied by 3. 135×3 = **405**. **Answer: 405.**
**Example 3 – Square numbers:** 1, 4, 9, 16, ?, 36. These are 1²,2²,3²,4²,5²,6². Missing number = 5² = **25**. **Answer: 25.**
**Example 4 – First differences:** 2, 6, 12, 20, 30, ? Differences: 4,6,8,10. Next is 12, so 30+12 = **42**. Alternative: these terms follow n(n+1); 6×7 = 42.
**Example 5 – Fibonacci-style:** 2, 3, 5, 8, 13, ? Each term is the sum of the previous two. 8+13 = **21**. **Answer: 21.**
**Example 6 – Alternating patterns:** 2, 10, 4, 20, 6, 30, ?, ? Odd positions: 2,4,6,**8**; even positions: 10,20,30,**40**. **Answer: 8, 40.**
## 4. Examination Shortcuts Differences are often the quickest starting point. When numbers grow rapidly, check multiplication, squares and cubes. If the series alternates between small and large numbers, split the odd and even positions. Never accept a rule that explains only the first few numbers but fails on the rest.
## 5. Textbook and Book-Back Progress **Class 6 Mathematics, Term III, Unit 5 – Information Processing; Exercise 5.1 Q2(i–iv), printed page 82, government SCERT English edition 2018.** The textbook provides four subquestions requesting the next three numbers. Three—Q2(i), Q2(ii) and Q2(iii)—are included with Tamil and English answers in tonight's separately labelled book-back batch; Q2(iv) remains pending. **Verification applies to the 2018 edition only; 2026–27 edition: source not yet verified.** The six worked examples are **original models**, not textbook quotations or authenticated TNPSC PYQs. **Verified Group IV PYQs: 0.**
## Revision Review on **3, 5, 9 and 16 November 2026** (+1/+3/+7/+14). Also review yesterday's Dice Reasoning lesson briefly.
## Push Notification **Title:** 🔢 TNPSC Group IV | Day 21 – Number Series! **Message:** Master differences, multiplication, squares, Fibonacci and alternating patterns with six fully solved examples in today's bilingual Aptitude lesson.
Sources: https://tnpsc.gov.in/static_pdf/syllabus/496_Group%20IV%20Syllabus.pdf https://cdn1.byjus.com/wp-content/uploads/2019/07/Tamil-Nadu-Class-6-Maths-Book-Term-3English.pdf
