Chapter 8 of the new Ganita Manjari book covers Sequences and Progressions. The Class 9 Maths Formula Sheet Chapter 8 Sequences and Progressions collects the term rules, the AP and GP formulas, and the sum of the first n natural numbers on one clean page for quick revision.
- Formulas inside: about 12 rules, from the nth term of an AP to the nth term of a GP.
- What they cover: explicit and recursive rules, special number sequences, and the two main progressions.
- Why one page helps: the AP, GP, and sum rules sit together, so revision before a test is fast.
This sheet is prepared by subject teachers, matched to the current 2026-27 NCERT, and checked line by line so a Class 9 student can trust every formula.
What Does the Class 9 Maths Sequences and Progressions Formula Sheet Cover?
The Class 9 Maths Formula Sheet Chapter 8 Sequences and Progressions covers the full set of rules in the chapter. You get term notation tn, the explicit rule tn=f(n), and the recursive rule that builds each term from the ones before it. It lists the Virahanka-Fibonacci rule, triangular and square numbers, and the sum of the first n natural numbers. It then gives the arithmetic progression: its nth term tn=a+(n-1)d and common difference d, and the geometric progression: its nth term tn=arn-1 and common ratio r. Every formula matches the book.
Video Walkthrough
Source: Physics Wallah Foundation on YouTube
Sequences and Progressions Class 9 Maths All Formulas at a Glance
The table below lists every formula for Chapter 8. Each formula cell is written in clean math so you can use it right away.
| Concept | Formula | What it means |
|---|---|---|
| Term notation | tn | The term in the nth position of the sequence. |
| Explicit rule | tn = f(n) | Find any term straight from its position n. |
| Recursive rule | t1 = a, tn = rule using tn-1 | Each term is built from the earlier term(s). |
| Virahanka-Fibonacci | Vn = Vn-1 + Vn-2 | Each term is the sum of the previous two. |
| Triangular numbers | tn = n(n+1)2 | Gives 1, 3, 6, 10, … |
| Square numbers | tn = n2 | Gives 1, 4, 9, 16, … |
| Sum of first n naturals | Sn = n(n+1)2 | Adds 1 + 2 + ⋯ + n in one step. |
| AP general form | a, a+d, a+2d, … | Start at a, add the common difference d. |
| AP common difference | d = tn - tn-1 | The fixed gap between neighbouring terms. |
| AP nth term | tn = a + (n-1)d | Any term of an AP from its position. |
| GP common ratio | r = tntn-1 | The fixed multiplier between neighbouring terms. |
| GP nth term | tn = a r n-1 | Any term of a GP from its position. |
When to Use Which Formula in Sequences and Progressions
Pick the right formula by reading how the sequence grows. This short list keeps the choice quick.
- If each term adds a fixed number, it is an AP; use tn = a + (n-1)d.
- If each term multiplies by a fixed number, it is a GP; use tn = a rn-1.
- If you must add 1 + 2 + ⋯ + n, use Sn = n(n+1)2.
- If a term depends on the ones before it, write a recursive rule.
- If each term is the sum of the previous two, it is a Virahanka-Fibonacci sequence.
- If you must check a value k is a term, solve the nth-term rule for n and see if it is a natural number.
Quick Facts for Sequences and Progressions
The cards below hold the facts students slip on most. Keep the Class 9 Maths Formula Sheet Chapter 8 Sequences and Progressions next to them while you revise, and the formulas will stick faster.
How will Collegedunia's Formula Sheet Help You with Sequences and Progressions?
Collegedunia builds the Class 9 Maths Formula Sheet Chapter 8 Sequences and Progressions as one printable page for fast revision.
- 2026-27 Ganita Manjari match: Every formula follows the new book, not the old chapter order.
- Plain meaning added: Each formula has a short line saying what it does.
- Teacher checked: Subject experts verify each AP, GP, and sum rule.
- Free PDF: Download the sheet and keep it ready for your Class 9 annual exam.
More Sequences and Progressions Maths Class 9 Resources
Use the links below to open the other Collegedunia resources for this chapter.
NCERT Formula Sheet for Class 9 Maths: All Chapters
Use the table below to open the Formula Sheet for any other chapter of the new Class 9 Maths book.
| Chapter | Resource |
|---|---|
| Chapter 1 | Coordinates Formula Sheet |
| Chapter 2 | Linear Polynomials Formula Sheet |
| Chapter 3 | The World of Numbers Formula Sheet |
| Chapter 4 | Algebraic Identities Formula Sheet |
| Chapter 5 | Circles Formula Sheet |
| Chapter 6 | Perimeter and Area Formula Sheet |
| Chapter 7 | Introduction to Probability Formula Sheet |
| Chapter 8 | Sequences and Progressions Formula Sheet |
Sequences and Progressions Class 9 Maths Formula Sheet FAQs
Ques. Where can I download the Sequences and Progressions Class 9 Maths Formula Sheet PDF?
Ans. You can download the Sequences and Progressions Class 9 Maths Formula Sheet PDF directly from this page. Both the Normal and HD versions are free.
Ques. How many formulas are in the Class 9 Maths Chapter 8 Sequences and Progressions Formula Sheet?
Ans. The sheet lists about 12 formulas, covering explicit and recursive rules, triangular and square numbers, the sum of the first n naturals, and the AP and GP nth-term rules.
Ques. Is this chapter part of the new 2026-27 Ganita Manjari book?
Ans. Yes. Sequences and Progressions is Chapter 8 of the new Ganita Manjari book for the 2026-27 syllabus, and it introduces AP and GP early to Class 9 students.
Ques. How many pages is the Sequences and Progressions Formula Sheet PDF?
Ans. The Formula Sheet PDF runs about 2 pages, with a full formula table and a quick-reference section for last-day revision.
Ques. What is the difference between an AP and a GP?
Ans. In an AP each term adds a fixed common difference d, so tn = a + (n-1)d. In a GP each term multiplies by a fixed common ratio r, so tn = a rn-1.
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