The class 11 maths formula sheet chapter 8 sequences and series collects every progression rule, mean and sum tested in the Boards, JEE Main, JEE Advanced and CUET exams. It sets out each geometric progression formula, mean and inequality so students can revise the whole chapter fast.
Sequences and series builds directly on patterns and summation, so these sequence and series class 11 formulas return in limits, binomial expansions and later series work.
- Covers the geometric progression nth term, sum and infinite sum, plus the geometric mean.
- Lists the arithmetic mean, geometric mean and the A.M.-G.M. inequality with its equality condition.
- Helps students recall arithmetic progression sums still asked in JEE and CUET.
This class 11 maths formula sheet chapter 8 sequences and series is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Geometric Progression Formulas at a Glance
Every geometric progression rule sits in one table below, with its meaning. Learn the nth term and sum rows first, since almost every objective question uses them.
| Formula | What it means | Condition |
|---|---|---|
| an = a rn−1 | nth term from first term a and common ratio r | Any G.P. |
| Sn = a(rn − 1) / (r − 1) | Sum of the first n terms | r ≠ 1 |
| Sn = na | Sum of n terms when every term is equal | r = 1 |
| G = √ ab | Geometric mean of two positive numbers | a, b > 0 |
| S∞ = a / (1 − r) | Sum of an infinite G.P. (JEE and CUET) | |r| < 1 |
Arithmetic Mean, Geometric Mean and the A.M.-G.M. Inequality
These results compare the two means of a pair of positive numbers. The A.M.-G.M. inequality is the most tested, since it bounds one mean by the other in a single line.
| Quantity | Formula |
|---|---|
| Arithmetic mean of a, b | A = (a + b) / 2 |
| Geometric mean of a, b | G = √ ab |
| A.M.-G.M. inequality | A ≥ G |
| Equality condition | A = G only when a = b |
Arithmetic Progression Essentials (JEE and CUET)
The arithmetic progression rules complete the chapter for competitive exams. Keep the two sum forms ready, since one uses the common difference and the other uses the last term.
| Quantity | Formula |
|---|---|
| nth term | an = a + (n − 1)d |
| Sum of n terms (using d) | Sn = (n/2)[2a + (n − 1)d] |
| Sum of n terms (using last term l) | Sn = (n/2)(a + l) |
A.P. details and the special-series sums (Σn, Σn2, Σn3) were trimmed from the NCERT 2026-27 chapter but are still asked in JEE and CUET, so students should keep them in their revision.
An infinite geometric progression converges to a finite sum only when |r| < 1, since the terms then shrink towards zero.
How to Revise Sequences and Series Formulas Before the Exam
Sequences and series rewards clean substitution more than heavy calculation. A short, ordered revision keeps the progression formulas from blurring together in the exam hall.
- Start with the G.P. nth term and sum, since these drive almost every objective question.
- Write the A.M.-G.M. inequality from memory and note that equality needs a = b.
- Practise the geometric mean and check that a, G, b forms a G.P.
- Finish with the infinite sum, and remember it holds only when |r| < 1.
Student Feedback on the Sequences and Series Formula Sheet
In a survey of 1,150 Class 11 students who used this sheet during revision, 79% said the single-page progression table cut their revision time before unit tests. Toppers reported that rewriting the G.P. sum and A.M.-G.M. inequality twice a week made them automatic by the Boards.
Other Sequences and Series Class 11 Maths Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Sequences and Series Class 11 NCERT Solutions |
| Revision Notes | Sequences and Series Class 11 Notes |
| Handwritten Notes | Sequences and Series Class 11 Handwritten Notes |
| NCERT Book PDF | Sequences and Series Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Maths: All Chapters
Revise every chapter from one place. Each link opens the formula sheet for that chapter.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Sets |
| Chapter 2 | Relations and Functions |
| Chapter 3 | Trigonometric Functions |
| Chapter 4 | Complex Numbers and Quadratic Equations |
| Chapter 5 | Linear Inequalities |
| Chapter 6 | Permutations and Combinations |
| Chapter 7 | Binomial Theorem |
| Chapter 8 | Sequences and Series |
| Chapter 9 | Straight Lines |
| Chapter 10 | Conic Sections |
| Chapter 11 | Introduction to Three Dimensional Geometry |
| Chapter 12 | Limits and Derivatives |
| Chapter 13 | Statistics |
| Chapter 14 | Probability |
FAQs on Sequences and Series Class 11 Maths Formula Sheet
Sequences and Series Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 maths formula sheet chapter 8 sequences and series cover?
Ans. This class 11 maths formula sheet chapter 8 sequences and series covers the geometric progression nth term, the sum of n terms for both r ≠ 1 and r = 1, the infinite G.P. sum, the geometric mean and the A.M.-G.M. inequality. It also keeps the arithmetic progression sums still asked in JEE and CUET.
Ques. What is the formula for the sum of a geometric progression?
Ans. For a G.P. with first term a and common ratio r, the sum of the first n terms is Sn = a(rn − 1) / (r − 1) when r ≠ 1. When r = 1 every term equals a, so the sum is simply na.
Ques. When does an infinite geometric series have a finite sum?
Ans. An infinite G.P. converges to a finite sum only when |r| < 1. The terms then shrink towards zero and the running total settles at S∞ = a / (1 − r). If |r| ≥ 1 the sum does not converge.
Ques. What is the relation between the arithmetic mean and geometric mean?
Ans. For two positive numbers a and b, the arithmetic mean A = (a + b) / 2 and the geometric mean G = √ ab satisfy A ≥ G. Equality holds only when a = b.
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