The NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Miscellaneous Exercise solve every mixed question of the chapter, 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.
The Miscellaneous Exercise blends every idea of the chapter and is the closest set to the board and entrance-exam level. It has 18 questions built around these skills:
- Mixing G.P. conditions with functions, roots of quadratics and A.M.–G.M. ratios.
- Summing special series such as 5 + 55 + 555 + ... and 2×4 + 4×6 + 6×8 + ...
- Solving real-life word problems on instalments, interest, depreciation and work.
Topics Covered in the Miscellaneous Exercise
The Miscellaneous Exercise pulls together the whole of Chapter 8, so students meet a wider mix of question styles than in Exercise 8.1 or Exercise 8.2. In the 2026-27 rationalised NCERT this exercise still carries the special-series and application questions that once sat in separate exercises, so it is the single best revision set for the chapter.
- G.P. proofs and conditions: using p-th, q-th, r-th terms, products and reciprocals of a G.P.
- A.M. and G.M.: ratio problems that give the two numbers from their arithmetic and geometric means.
- Special series: summing numbers like 5 + 55 + 555 + ... by relating them to a G.P.
- Sequences of products: the series 2×4 + 4×6 + 6×8 + ... whose general term is a product.
- Applications: instalment buying, simple interest, chain letters, depreciation and workforce problems.
Important: a series such as 5 + 55 + 555 + ... is not itself a G.P. Rewrite each term using (10k − 1)/9, and the sum then reduces to a standard G.P. sum.
Question-wise Breakdown of the Miscellaneous Exercise
The NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Miscellaneous Exercise solve all 18 questions in order. The table below groups them by type so students can plan their revision. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1 to Q5 | G.P. conditions with a function, sum, and odd-place terms | Setting up G.P. equations |
| Q6 to Q10 | Prove terms are in G.P. and use A.M.–G.M. ratios | Proofs and A.M.–G.M. |
| Q11 to Q12 | Sum special series like 5 + 55 + 555 + ... and 2×4 + 4×6 + ... | Special series |
| Q13 to Q18 | Word problems on instalments, interest, chain letters, depreciation, work | Applications of A.P. and G.P. |
Because the questions are mixed, students should first name the pattern (G.P., special series or application) before choosing a formula.
Key Formulas and Definitions for the Miscellaneous Exercise
The Miscellaneous Exercise reuses the main results of the chapter. The table below lists the ones needed most often here.
| Result | Formula |
|---|---|
| General (nth) term of a G.P. | an = arn−1 |
| Sum of n terms of a G.P. (r ≠ 1) | Sn = a(rn − 1)/(r − 1) |
| Geometric mean of a and b | G = √(ab) |
| A.M. and G.M. of a and b | A = (a + b)/2, G = √(ab), with A ≥ G |
| Repunit trick for 5 + 55 + 555 + ... | each term = (10k − 1)/9 |
| Number of ancestors / growth | doubling gives a G.P. with r = 2 |
Tip: in A.M.–G.M. ratio problems, let the two numbers be a and b, form A = (a + b)/2 and G = √(ab), then use (a − b)2 = (a + b)2 − 4ab to reach the answer quickly.
Common Mistakes in the Miscellaneous Exercise
Students lose marks in the Miscellaneous Exercise by forcing the wrong pattern onto a question. The list below covers the errors that show up most often in tests on the NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Miscellaneous Exercise.
- Treating 5 + 55 + 555 + ... as a plain G.P. Each term must first be rewritten with the (10k − 1)/9 trick.
- Mixing simple interest with compound interest in the instalment and deposit word problems.
- In A.M.–G.M. ratio questions, forgetting to take both signs of (a − b) when solving.
- In the series 2×4 + 4×6 + ..., using a wrong general term instead of the product form 2n(2n + 2).
Practice Questions for the Miscellaneous Exercise
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 the Miscellaneous Exercise.
Practice Card: Solved Practice Questions for Class 11 Maths Sequences and Series Miscellaneous Exercise — 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 this Miscellaneous Exercise. Use the table to revisit the earlier exercises once the Miscellaneous set is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 8.1 | Class 11 Maths Sequences and Series Exercise 8.1 Solutions |
| Exercise 8.2 | Class 11 Maths Sequences and Series Exercise 8.2 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 8,470 Class 11 students conducted before the 2026 exams, 66% of students said the special-series questions (Q11 and Q12) of the Miscellaneous Exercise were the ones they revisited most, while the instalment and interest word problems were rated the most exam-relevant.
FAQs on NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Miscellaneous Exercise
Sequences and Series NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in the Class 11 Maths Chapter 8 Sequences and Series Miscellaneous Exercise?
Ans. The Miscellaneous Exercise has 18 questions that mix Geometric Progression proofs, A.M.–G.M. ratios, special-series sums and real-life word problems on instalments, interest and depreciation. It is the best all-round revision set for Chapter 8.
Ques. How do you sum a series like 5 + 55 + 555 + ... in the Miscellaneous Exercise?
Ans. The series 5 + 55 + 555 + ... is not a G.P. by itself. Take out 5/9 and write each term as (10k − 1), so the sum becomes 5/9 times a G.P. of 10, 100, 1000, ... minus n ones. Question 11 of the Miscellaneous Exercise is solved this way.
Ques. Is the Miscellaneous Exercise important for CBSE Boards and JEE?
Ans. Yes. The Miscellaneous Exercise combines every idea of Sequences and Series and includes proof and application questions in the style of CBSE Boards, JEE Main, JEE Advanced and CUET. Working through it is the best way to test full command of the chapter.
Ques. How are A.M. and G.M. used in the Miscellaneous Exercise?
Ans. Several questions give the A.M. and G.M., or their ratio, of two positive numbers and ask for the numbers. Using A = (a + b)/2, G = √(ab) and the identity (a − b)2 = (a + b)2 − 4ab, the pair is found quickly. Question 10 of the Miscellaneous Exercise follows this method.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Miscellaneous Exercise free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series Miscellaneous Exercise 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.
Comments