Class 9 Maths Chapter 8, Predicting What Comes Next: Exploring Sequences and Progressions, is the last chapter of Ganita Manjari Part I. It starts from sequences you already know (natural, odd and triangular numbers) and finds rules that predict any term, leading to arithmetic progressions, the sum of the first n natural numbers and geometric progressions, with a bouncing ball and the Sierpiński triangle as examples.
What Class 9 Maths Chapter 8 Covers
8.1 to 8.3 Sequences and Their Rules separate an explicit rule, which gives a term from its position (for example uₙ = 2n – 1), from a recursive rule, which builds each term from the previous ones, and test whether numbers like 308 and 473 belong to a sequence.
8.4 Arithmetic Progressions uses a growing pattern of squares to reach tₙ = a + (n – 1)d, with common difference d.
8.5 Sum of the First n Natural Numbers derives n(n + 1)/2, the formula behind the triangular numbers.
8.6 Geometric Progressions covers sequences with a common ratio r and tₙ = arⁿ⁻¹, including a ball that rises to a fixed fraction of its height after each bounce, and fractals such as the Sierpiński triangle.
Exercises in Chapter 8
- Exercise Sets 8.1 to 8.3 plus short in-text exercises, such as finding the 53rd term from uₙ = 2n – 1.
- End-of-Chapter Exercises, then a chapter summary, with graph paper pages at the end of the PDF.
Read Class 9 Maths Chapter 8 Online
More Chapters
- Previous: Chapter 7: The Mathematics of Maybe: Introduction to Probability
- Hindi medium: Class 9 Maths Chapter 8 PDF in Hindi (अगले पद का पूर्वानुमान — अनुक्रमों और श्रेढ़ियों का अन्वेषण)
- All Maths chapters and the other Class 9 books: Class 9 NCERT books 2026-27
- All Class 1 to 12 NCERT Textbooks: NCERT Books PDF (Class 1–12)
FAQ
Are AP and GP in Class 9 now?
Yes. In the 2026-27 book Ganita Manjari, Chapter 8 covers arithmetic progressions (tₙ = a + (n – 1)d) and geometric progressions (tₙ = arⁿ⁻¹).
What is the sum of the first n natural numbers?
n(n + 1)/2. Chapter 8 derives it in section 8.5 and shows it is also the nth triangular number.