Class 9 Maths Chapter 8 – Predicting What Comes Next: Exploring Sequences and Progressions | Ganita Manjari
Chapter 8 – Predicting What Comes Next: Exploring Sequences and Progressions explores patterns in numbers and other objects and shows how mathematical rules can be used to predict what comes next.
Students begin with familiar sequences such as natural numbers, odd numbers, triangular numbers and square numbers. They then develop rules for sequences and explore explicit and recursive formulas.
The chapter progresses to arithmetic progressions (APs) and geometric progressions (GPs), connecting these ideas with visual patterns, graphs, fractals and real-life situations.
Table of Contents
📅 Last Updated: August 2026
📘 Syllabus: Based on the latest CBSE Class 9 (2026–27) syllabus
✅ Updated Resources Include:
- Chapter-wise Study Notes
- Free PDF Downloads
- MCQs
Chapter Overview
| Information | Details |
|---|---|
| Class | 9 |
| Subject | Maths |
| Textbook | Ganita Manjari |
| Chapter | 8 |
| Chapter Title | Predicting What Comes Next: Exploring Sequences and Progressions |
| Academic Session | 2026–27 |
| Resources | Notes, Worksheets, Questions, Tests & Revision |
📝 What You'll Learn in This Chapter
- 🔢 Understand sequences as ordered lists of numbers.
- 🔍 Identify patterns in different number sequences.
- 📈 Predict the next terms of a sequence.
- ✏️ Find the nth term using an explicit rule.
- 🔄 Understand recursive rules for generating sequences.
- 🧮 Explore the Virahānka–Fibonacci sequence.
- ➕ Understand Arithmetic Progressions (APs).
- 📐 Find the common difference of an AP.
- 🔢 Find the nth term of an AP.
- 📊 Visualise arithmetic progressions using graphs.
- ➕ Find the sum of the first n natural numbers.
- 🔢 Explore Geometric Progressions (GPs).
- ✖️ Find the common ratio of a GP.
- 📈 Find the nth term of a GP.
- 🔄 Write explicit and recursive rules for GPs.
- 🌳 Explore geometric patterns and fractals, including the Sierpiński triangle.
- 🏀 Apply geometric progressions to real-life situations such as bouncing balls.
- 🧠 Use sequences and progressions to solve mathematical and real-life problems.
🎯 Learning Outcomes
After completing this chapter, students will be able to:
- Define and identify sequences.
- Recognise patterns and predict subsequent terms.
- Find terms using an explicit formula.
- Generate terms using a recursive formula.
- Identify and work with arithmetic progressions.
- Find the common difference and nth term of an AP.
- Calculate the sum of the first n natural numbers.
- Identify and work with geometric progressions.
- Find the common ratio and nth term of a GP.
- Represent sequences and progressions using tables, patterns and graphs.
- Apply APs and GPs to mathematical and real-life situations.
- Use recursive and explicit rules to analyse sequences.
The textbook defines an AP using a constant common difference and gives the nth-term formula . It similarly defines a GP through a constant common ratio and gives its nth-term form.
📌 Key Topics
- Introduction to Sequences
- Number Patterns
- Natural, Odd, Triangular and Square Number Sequences
- Explicit Rules for Sequences
- Recursive Rules
- Virahānka–Fibonacci Sequence
- Arithmetic Progressions
- Common Difference
- Nth Term of an AP
- Visualising an AP
- Sum of the First n Natural Numbers
- Geometric Progressions
- Common Ratio
- Nth Term of a GP
- Explicit and Recursive Rules for GPs
- Sierpiński Triangle
- Geometric Patterns and Fractals
- Applications of Geometric Progressions
⭐ Class 9 Maths Chapter 8 Study Resources
🧬 Diagrams
Coordinate graphs, geometric figures and visual representations to help understand the chapter.
📌 Important Questions
Most important questions to prepare for exams and chapter revision.
🎯 Competency-Based Questions
Application-focused questions designed to develop deeper understanding.
🎁 Free Class 9 Worksheets
Practise sequences, arithmetic progressions, geometric progressions, nth-term formulas and related concepts with our free printable Chapter 8 worksheet.
Class 9 Maths – Chapter 8: Free Sample Worksheet10 Questions + Answer Key
NCERT Exercise Solutions – Ganita Manjari
Practise the questions from Chapter 8 and check your answers with our step-by-step solutions.
EX 8.1
EX 8.2
EX 8.3
End-of-Chapter Exercises
Why Students Choose Our Class 9 Maths Resources?
2026–27 Focused
Printable PDFs
Original Practice
Chapter-Wise Resources
Mobile Friendly
Answer Keys
❓FAQ
Q1. What textbook is used for Class 9 maths in 2026–27?
The new NCERT Ganita Manjari textbook is used for Class 9 Maths for the 2026–27 academic session.
Q2. Which chapter is this page about?
This page is about Chapter 8 – Predicting What Comes Next: Exploring Sequences and Progressions from Ganita Manjari.
Q3. Are these NCERT textbook copies?
No. The study resources and practice materials on this page are supplementary resources created to support students’ learning. The NCERT textbook itself is not reproduced here.
Q4. Are the worksheets free?
Explain which resources are free and which may be available as complete practice resources.
Q5. Are answer keys included?
Explain depending on the particular resource.
Q6. Are these resources suitable for school revision?
Yes.
Q7. Will more Chapter 8 resources be added?
More Class 9 Maths Chapter 8 resources may be added in the future to provide additional practice and revision support.
Q8. How many exercise sets are there in Chapter 8?
Chapter 8 has three exercise sets: EX 8.1, EX 8.2 and EX 8.3, followed by a separate End-of-Chapter Exercises section.
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