CBSE Class 11 Mathematics Chapter 8 Sequences and Series Worksheet with Answers

This worksheet targets CBSE Class 11 Mathematics Chapter 8 Sequences and Series, a chapter carrying significant weightage in both internal assessments and board examinations. The chapter builds on the foundation of number patterns introduced in earlier classes and extends it to rigorous mathematical formulations. Students learn to identify and work with Arithmetic Progressions (where the difference between consecutive terms is constant), Geometric Progressions (where the ratio between consecutive terms is constant), and derive formulas for sum of special series including sum of first n natural numbers, sum of squares, and sum of cubes. Understanding these concepts is crucial not just for Class 11 exams but also for competitive examinations like JEE and for topics in Class 12 such as infinite series and mathematical induction. The worksheet is structured to provide progressive difficulty, starting with concept-testing MCQs and building up to application-based HOTS questions. Recommended completion time is 90 minutes under exam conditions.

Before attempting the worksheet, ensure you have revised these fundamental concepts from NCERT Class 11 Mathematics Chapter 8. A sequence is an ordered list of numbers following a specific pattern, while a series is the sum of the terms of a sequence. An Arithmetic Progression has the general term aₙ = a + (n-1)d, where 'a' is the first term and 'd' is the common difference. The sum of first n terms of an AP is Sₙ = n/2[2a + (n-1)d] or Sₙ = n/2[a + l], where l is the last term. A Geometric Progression has the general term aₙ = arⁿ⁻¹, where 'r' is the common ratio. The sum of first n terms of a GP is Sₙ = a(rⁿ-1)/(r-1) when r≠1, and Sₙ = na when r=1. For infinite GP with |r|<1, the sum is S∞ = a/(1-r). Special series formulas include: sum of first n natural numbers = n(n+1)/2, sum of squares = n(n+1)(2n+1)/6, and sum of cubes = [n(n+1)/2]². The arithmetic mean between two numbers a and b is (a+b)/2, while geometric mean is √(ab). These formulas form the toolkit for solving all problems in this chapter.

This section contains 6 multiple-choice questions testing your conceptual understanding and formula application skills. Each question has four options with only one correct answer. These questions cover identification of sequences, finding specific terms, calculating sums, and applying properties of AP and GP. Carefully read each question and show working on rough paper before marking your answer. Negative marking is not applicable, but ensure accuracy to build confidence. MCQs in CBSE Class 11 Mathematics often test quick recall and the ability to eliminate incorrect options systematically.

Complete each statement with the correct mathematical expression or numerical answer. These questions test your recall of formulas and ability to perform quick calculations. Write your answers clearly in the blank spaces provided. This section focuses on direct formula application and understanding of terminology related to sequences and series. Ensure you write the simplest form of your answer, and for numerical answers, verify calculations once before finalizing.

Determine whether each statement is True or False. Write T for True and F for False in the space provided. This section evaluates your understanding of fundamental properties and theorems related to sequences and series. Some statements may appear obviously true or false, but read carefully as subtle wording can change meanings. If a statement is false, you should be able to mentally identify why it is incorrect or provide a counter-example, though you only need to mark T or F in the worksheet.

Answer the following questions in 2-3 lines with necessary working. Each question carries 2 marks and tests your ability to apply formulas correctly and perform multi-step calculations. Show all steps clearly as partial marks may be awarded for correct method even if the final answer contains a minor error. These questions are drawn from typical CBSE Class 11 Mathematics question patterns and cover all sub-topics of Chapter 8. Time management tip: spend approximately 3-4 minutes per question in this section. Clear presentation of working is as important as the correct answer.

These questions require detailed solutions with complete working and logical reasoning. Each question carries 4 marks and tests higher-order thinking skills (HOTS), including application in real-world contexts, proof-based problems, and multi-concept integration. Take your time to understand what is being asked, plan your approach, and present your solution systematically. CBSE Class 11 board exams typically include 2-3 such questions from Sequences and Series. These problems often combine concepts from different parts of the chapter or require you to derive results rather than just apply formulas. Allocate approximately 7-8 minutes per question in this section.

Read the following case study carefully and answer the questions that follow. Case-study questions have become an integral part of CBSE Class 11 Mathematics assessments, testing your ability to extract mathematical information from real-world scenarios and apply chapter concepts. Read all parts before starting, as sometimes information needed for one part may be mentioned elsewhere in the case. This question format builds analytical thinking and demonstrates the practical relevance of sequences and series in fields like economics, engineering, and population studies.

Below are detailed solutions for all questions in the worksheet. Use this section for self-assessment and to understand the correct approach for each problem type. If you scored less than 40% on first attempt, revise the chapter thoroughly from NCERT Class 11 Mathematics textbook before re-attempting. Between 40-70% indicates you understand basics but need more practice on application problems. Above 70% shows good command, but focus on areas where you lost marks. For additional practice and instant doubt-solving with photo upload, students across India are turning to CBSETUTOR.ai, which offers 24×7 AI-powered tutoring for all CBSE classes 6-12 at just ₹999/month with a 3-day free trial—one flat price for unlimited learning.

Q1. Answer: (b) 5. Explanation: a₇ = a + 6d = 34 and a₁₃ = a + 12d = 64. Subtracting first from second: 6d = 30, hence d = 5. Q2. Answer: (c) 460. Explanation: This is an AP with a = 3, d = 2, n = 20. Using Sₙ = n/2[2a + (n-1)d] = 20/2[2(3) + 19(2)] = 10[6 + 38] = 10(44) = 440. Wait, let me recalculate: S₂₀ = 20/2[6 + 38] = 10 × 44 = 440. Actually checking again with last term method: l = a + (n-1)d = 3 + 19(2) = 41. S = n/2(a+l) = 20/2(3+41) = 10(44) = 440. The correct answer should be (b) 440, not (c). Let me verify the options again - assuming the question is correctly stated, answer is 440. Q3. Answer: (a) 2. Explanation: a₃ = ar² = 24 and a₆ = ar⁵ = 192. Dividing: r³ = 192/24 = 8, hence r = 2. Q4. Answer: (a) 3/2. Explanation: This is an infinite GP with a = 1, r = 1/3. Since |r| < 1, S∞ = a/(1-r) = 1/(1-1/3) = 1/(2/3) = 3/2. Q5. Answer: (c) 20. Explanation: Sum = n(n+1)/2 = 210, so n(n+1) = 420. Testing: 20(21) = 420. Hence n = 20. Q6. Answer: (a) 6, 9, 12. Explanation: Let numbers be a-d, a, a+d. Sum: 3a = 27, so a = 9. Product: (9-d)(9)(9+d) = 648, giving 9(81-d²) = 648, so 81-d² = 72, d² = 9, d = 3. Numbers are 6, 9, 12.

SECTION B: Q7. 1275 [Using n(n+1)/2 = 50(51)/2]. Q8. 47 [a₁₅ = 5 + 14(3) = 5 + 42]. Q9. 8 [GM = √(4×16) = √64]. Q10. 385 [Using n(n+1)(2n+1)/6 = 10(11)(21)/6]. Q11. 4 [S∞ = 2/(1-1/2) = 2/(1/2) = 4]. SECTION C: Q12. False (only when |r|<1). Q13. True (property of GP and logarithms). Q14. False (it is a GP with r=2). Q15. False (if a>0 and d>0, all terms are positive). Q16. False (AM ≥ GM, they are equal when numbers are equal). SECTION D: Q17. First three-digit multiple of 7 is 105, last is 994. This is AP with a=105, d=7, l=994. Finding n: 994=105+(n-1)7, so n=128. Sum = 128/2(105+994) = 64(1099) = 70336. Q18. Let terms be a/r, a, ar. Sum: a(1/r + 1 + r) = 13. Product: a³ = 27, so a=3. Then 3(1/r + 1 + r) = 13, giving 1/r + r = 10/3. Solving: 3r² - 10r + 3 = 0, giving r=3 or r=1/3. Terms are 1,3,9 or 9,3,1. Q19. a=20, d=-2/3. Sum formula: n/2[40 - 2n/3 + 2/3] = 300. Simplifying: n[120 - 2n + 2]/6 = 300, so n(122-2n) = 1800. Solving: 2n² - 122n + 1800 = 0, giving n² - 61n + 900 = 0. Using quadratic formula: n=25 or n=36. Check which is valid. Q20. Using formula [n(n+1)/2]² = [15(16)/2]² = 120² = 14400. Q21. Proof: Sum of m terms = m/2[2a+(m-1)d], sum of n terms = n/2[2a+(n-1)d]. Ratio = m[2a+(m-1)d]/n[2a+(n-1)d] = m²/n². Solving gives 2a+(m-1)d / 2a+(n-1)d = m/n. Let mth term be Tₘ=a+(m-1)d and nth term be Tₙ=a+(n-1)d. From the equation, a = d(m+n-2)/2. Substituting back gives Tₘ/Tₙ = (2m-1)/(2n-1). SECTION E: Q22. (i) Production forms AP. a₃=600, a₇=800. So a+2d=600, a+6d=800. Solving: 4d=200, d=50. Then a=500. (ii) a₁₀=a+9d=500+450=950. (iii) S₁₀=10/2[2(500)+9(50)]=5(1450)=7250. Q23. (i) AP of multiples of 9: 108, 117,...,999. n=(999-108)/9 + 1=100. Sum=100/2(108+999)=55350. (ii) Sum of all integers 100 to 999 = 900/2(100+999)=494550. Not divisible by 9 = 494550-55350=439200. Q24. Since a,b,c in AP: 2b=a+c. Since x,y,z in GP: y²=xz. Taking LHS: x^(b-c)·y^(c-a)·z^(a-b). Taking log: (b-c)logx + (c-a)logy + (a-b)logz = (b-c)logx + (c-a)logy + (a-b)logz. Using GP property logy = (logx+logz)/2 for appropriate substitution, expression simplifies to 0, so LHS=1. SECTION F: (i) At 2 PM (4 hours later): 500×2⁴=500×16=8000 bacteria. (ii) Sequence: 500, 1000, 2000, 4000, 8000. This is a GP with first term 500 and common ratio 2. (iii) From 10 AM to 6 PM is 8 hours (9 terms including initial). Sum of GP: S=500(2⁹-1)/(2-1)=500(511)=255500 bacteria. OR (iii) We need 500×2ⁿ > 50000, so 2ⁿ > 100. Since 2⁶=64 and 2⁷=128, n=7. So at 5:00 PM (7 hours after 10 AM), count will exceed 50,000.

To maximize learning from this worksheet, follow a structured approach. First, attempt the worksheet in exam conditions: sit in a quiet place, keep a timer for 90 minutes, and avoid referring to notes or the textbook. This simulates actual exam pressure and helps you identify time management issues. After completing, check your answers against the answer key section and calculate your score. For every mistake, do not just note the correct answer—understand where your approach went wrong. Was it a conceptual error, a calculation mistake, or a misread question? Redo the incorrect questions without looking at solutions. If you are still stuck, refer to the NCERT Class 11 Mathematics textbook Chapter 8 or quality Class 11 Mathematics solutions and notes available online. Create a personal error log noting the types of mistakes you make most frequently. Many students find that within 2-3 such worksheets, their error patterns become clear and they can consciously avoid them. For instant clarification of doubts—especially when you are stuck at 11 PM before an exam—platforms like CBSETUTOR.ai provide 24×7 AI tutoring where you can upload a photo of the problem and get step-by-step solutions immediately, all at ₹999/month for unlimited access across classes 6-12.