The NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Exercise 8.2 solve every question of the Geometric Progression exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 8.2 is the longest exercise of the chapter and covers the full theory of a Geometric Progression (G.P.). It has 32 questions built around these skills:
- Using the general term an = arn−1 to find any term of a G.P.
- Applying the sum of n terms formula and inserting geometric means.
- Proving relations and solving word problems on ratio, product and A.M.–G.M.
Topics Covered in Exercise 8.2
This exercise builds the complete toolkit for a Geometric Progression, a sequence in which each term after the first is a fixed multiple (the common ratio r) of the one before it. Exercise 8.2 moves from finding terms to summing them and then to proofs. Note that in the 2026-27 rationalised NCERT there is no longer a separate Arithmetic Progression exercise; Chapter 8 now runs Exercise 8.1 (sequences), Exercise 8.2 (G.P.) and the Miscellaneous Exercise, so the G.P. work sits here.
- General term: using an = arn−1 to find a term or to identify which term equals a given value.
- Sum of n terms: Sn = a(rn − 1)/(r − 1) for r ≠ 1.
- Geometric mean: inserting one or more G.M.s between two numbers so the list stays in G.P.
- Relationship between A.M. and G.M.: using A ≥ G and identities on two positive numbers.
- Word problems: bacteria growth, compound interest style ratios and proofs with p, q, r terms.
Important: the sum formula is valid only for r ≠ 1. When r = 1 every term equals a, so the sum is simply Sn = na.
Question-wise Breakdown of Exercise 8.2
The NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Exercise 8.2 solve all 32 questions in order. The table below groups the questions by type so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1 to Q6 | Find given terms, or which term equals a value, using an = arn−1 | General term of a G.P. |
| Q7 to Q11 | Find the sum to a stated number of terms of a G.P. | Sum of n terms |
| Q12 to Q16 | Use sum and product conditions to find the terms and common ratio | Forming and solving equations |
| Q17 to Q25 | Prove standard results on p-th, q-th, r-th terms and products | Proofs with a G.P. |
| Q26 to Q32 | Insert geometric means, apply A.M.–G.M. and solve word problems | G.M. and applications |
Because the exercise is long, students should attempt it in these blocks rather than all at once.
Key Formulas and Definitions for Exercise 8.2
Exercise 8.2 uses a small set of G.P. formulas repeatedly. Students should memorise the table below before starting.
| Result | Formula |
|---|---|
| General (nth) term of a G.P. | an = arn−1 |
| Common ratio | r = ak+1 / ak |
| Sum of n terms (r ≠ 1) | Sn = a(rn − 1)/(r − 1) = a(1 − rn)/(1 − r) |
| Sum of n terms (r = 1) | Sn = na |
| Geometric mean of a and b | G = √(ab) |
| n G.M.s between a and b | r = (b/a)1/(n+1) |
| A.M.–G.M. inequality | A ≥ G, where A = (a + b)/2 and G = √(ab) |
Tip: when three terms are in G.P., take them as a/r, a, ar. The product then becomes a3, which turns a hard product condition into a single easy equation.
Common Mistakes in Exercise 8.2
Students lose marks in Exercise 8.2 on sign errors and misused formulas. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Exercise 8.2.
- Using the r ≠ 1 sum formula when r = 1. If the common ratio is 1, the sum is na, not the fraction form.
- Forgetting that a G.P. can have a negative common ratio, which flips the sign of alternate terms.
- Writing the general term as arn instead of arn−1, which shifts every term by one place.
- Dropping the second root when a squared or quadratic condition on r gives two valid values.
Practice Questions for Exercise 8.2
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 8.2.
Practice Card: Solved Practice Questions for Class 11 Maths Sequences and Series Exercise 8.2 — attempt each question, then check the worked solution.
Other Exercises of Chapter 8 Sequences and Series
Chapter 8 Sequences and Series has two exercises plus a Miscellaneous Exercise. Use the table to move between exercises once Exercise 8.2 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 8.1 | Class 11 Maths Sequences and Series Exercise 8.1 Solutions |
| Miscellaneous Exercise | Class 11 Maths Sequences and Series Miscellaneous Exercise Solutions |
More Class 11 Maths Sequences and Series Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 8 Sequences and Series are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Sequences and Series Notes |
| Handwritten Notes | Class 11 Maths Sequences and Series Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Sequences and Series NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | You are here |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 10,320 Class 11 students conducted before the 2026 exams, 72% of students rated the proof questions (Q17 to Q25) of Exercise 8.2 as the hardest, while the direct sum-of-n-terms problems were the most attempted in board practice.
FAQs on NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Exercise 8.2
Sequences and Series NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 8 Sequences and Series Exercise 8.2?
Ans. Exercise 8.2 has 32 questions, all based on Geometric Progression. They range from finding terms with an = arn−1 and summing n terms, to inserting geometric means, proving standard results and solving growth-based word problems.
Ques. What is the formula for the sum of n terms of a G.P.?
Ans. For a G.P. with first term a and common ratio r ≠ 1, the sum of n terms is Sn = a(rn − 1)/(r − 1), which can also be written as a(1 − rn)/(1 − r). When r = 1 the terms are all equal, so Sn = na. Questions 7 to 11 of Exercise 8.2 use this formula directly.
Ques. What is the geometric mean of two numbers in Exercise 8.2?
Ans. The geometric mean of two positive numbers a and b is √(ab), and a, G, b then form a G.P. To insert n means between a and b, the common ratio is r = (b/a)1/(n+1). Questions 26 and 27 of Exercise 8.2 apply this idea.
Ques. How do you take three terms in G.P. to make problems easier?
Ans. When a question gives the product or sum of three terms in G.P., writing them as a/r, a, ar keeps the algebra short. The product of the three is a3, so a product condition gives a at once. Question 12 of Exercise 8.2, on a sum of 39/10 and product 1, is solved this way.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Exercise 8.2 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Exercise 8.2 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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