CBSE Sequence and Series Class 11 MCQ with Answers

Improve your grasp of sequences and series with our detailed MCQs for Class 11 Mathematics Chapter 8. This chapter covers essential concepts like sequences, types of series, and their applications, making it a crucial part of your maths curriculum. Our Sequence and Series class 11 MCQs are designed to help you understand arithmetic and geometric progressions, ensuring you are well-prepared and confident in your studies.

Our collection of sequence and series class 11 MCQs with answers covers a wide range of topics, from basic sequences to complex series calculations. Each question aligns with the Class 11 CBSE syllabus, providing a valuable resource for revision and practice. Prepare effectively for your exams with our MCQs, which enhance your learning and boost your academic performance. You can also download NCERT solutions for Class 11 Mathematics to further solidify your understanding of the concepts.

Sequence and Series Class 11 MCQ Questions with Answers

1. If the first term of an AP is 5 and the common difference is 3, the 10th term is:
   a) 32
   b) 35
   c) 27
   d) 38
   Answer: b) 32
2. The nth term of the AP 2, 5, 8, 11,… is:
   a) 2n + 1
   b) 3n – 1
   c) 3n + 2
   d) 2n – 1
   Answer: b) 3n – 1
3. The sum of first 20 natural numbers is:
   a) 200
   b) 190
   c) 210
   d) 220
   Answer: c) 210
4. If 7th term of an AP is 20 and 13th term is 38, the common difference is:
   a) 2
   b) 3
   c) 4
   d) 5
   Answer: c) 3
5. The sum of first 50 odd natural numbers is:
   a) 2500
   b) 2550
   c) 2600
   d) 2400
   Answer: a) 2500
6. If the first term of a GP is 3 and common ratio is 2, the 5th term is:
   a) 48
   b) 24
   c) 36
   d) 32
   Answer: a) 48
7. The sum of first 4 terms of the GP 2, 4, 8, … is:
   a) 30
   b) 32
   c) 28
   d) 26
   Answer: c) 30
8. In a GP, if a = 1 and r = ½, then S∞ = ?
   a) 2
   b) 1
   c) ½
   d) 4
   Answer: a) 2
9. If the 3rd term of a GP is 9 and 6th term is 729, the common ratio is:
   a) 6
   b) 9
   c) 3
   d) 27
   Answer: c) 3
10. The 10th term of GP 5, 15, 45, … is:
    a) 98415
    b) 98405
    c) 98515
    d) 98505
    Answer: a) 98415
11. If a, b, c are in AP, then 1/a, 1/b, 1/c are in:
    a) HP
    b) GP
    c) AP
    d) None
    Answer: a) HP
12. The nth term of HP is reciprocal of nth term of:
    a) AP
    b) GP
    c) HP itself
    d) None
    Answer: a) AP
13. The 5th term of HP whose first term is 1 and common difference of corresponding AP is 2, is:
    a) 1/9
    b) 1/5
    c) 1/7
    d) 1/3
    Answer: a) 1/9
14. The sum of first n terms of AP is 3n² + 2n. Its common difference is:
    a) 6
    b) 3
    c) 2
    d) 4
    Answer: a) 6
15. If S = a/(1–r), |r| < 1, then the series is:
    a) AP
    b) Finite GP
    c) Infinite GP
    d) HP
    Answer: c) Infinite GP
16. Which of the following series is divergent?
    a) 1 + ½ + ¼ + ⅛ + …
    b) 1 + 2 + 4 + 8 + …
    c) 2 + 4 + 6 + 8 + …
    d) Both b and c
    Answer: d) Both b and c
17. If the sum of first n terms of a series is n², the nth term is:
    a) n² – (n–1)²
    b) 2n – 1
    c) 2n + 1
    d) Both a and b
    Answer: d) Both a and b
18. If the first and last terms of an AP are 10 and 100, with common difference 5, the number of terms is:
    a) 20
    b) 19
    c) 18
    d) 15
    Answer: b) 19
19. The sum of first 7 terms of GP 2, 6, 18, … is:
    a) 2186
    b) 2184
    c) 2182
    d) 2190
    Answer: b) 2184
20. The sequence log a, log a², log a³,… is:
    a) AP
    b) GP
    c) HP
    d) None
    Answer: a) AP
21. The sum of first 15 terms of AP: 2, 5, 8,… is:
    a) 330
    b) 345
    c) 360
    d) 375
    Answer: a) 330
22. If the 1st term is 7 and 4th term is 19, the common difference is:
    a) 2
    b) 3
    c) 4
    d) 5
    Answer: d) 4
23. The 20th term of an AP whose 7th term is 13 and 12th term is 23 is:
    a) 43
    b) 40
    c) 45
    d) 48
    Answer: b) 40
24. The sum of first n natural numbers is given by:
    a) n(n+1)
    b) n(n–1)/2
    c) n(n+1)/2
    d) n²/2
    Answer: c) n(n+1)/2
25. If the sum of first n terms of an AP is 5n² + 3n, its 10th term is:
    a) 103
    b) 101
    c) 105
    d) 100
    Answer: a) 103
26. The 7th term of GP 3, 6, 12,… is:
    a) 128
    b) 192
    c) 96
    d) 256
    Answer: b) 192
27. The sum of first n terms of GP a, ar, ar²,… is:
    a) (a(1–rⁿ))/(1–r), r ≠ 1
    b) (a(1–r))/(1–rⁿ), r ≠ 1
    c) (a(rⁿ–1))/(r–1), r ≠ 1
    d) Both a and c
    Answer: d) Both a and c
28. The 8th term of GP whose 1st term is 2 and r = 3 is:
    a) 1458
    b) 6561
    c) 729
    d) 2187
    Answer: a) 1458
29. If the first term is 81 and r = 1/3, the 5th term is:
    a) 3
    b) 9
    c) 27
    d) 1
    Answer: a) 3
30. If the 4th term of a GP is 16 and 7th term is 128, the common ratio is:
    a) 2
    b) 3
    c) 4
    d) 5
    Answer: a) 2
31. If 1, ½, ⅓,…, 1/n are in sequence, it is:
    a) AP
    b) GP
    c) HP
    d) None
    Answer: c) HP
32. The harmonic mean between 4 and 12 is:
    a) 8
    b) 6
    c) 12
    d) 9
    Answer: b) 6
33. If a, b, c are in GP, then reciprocals 1/a, 1/b, 1/c are in:
    a) AP
    b) GP
    c) HP
    d) None
    Answer: c) HP
34. The harmonic mean between 2 and 18 is:
    a) 6
    b) 9
    c) 18
    d) 8
    Answer: b) 6
35. If a and b are positive numbers, the HM of a and b is always:
    a) Greater than GM
    b) Equal to GM
    c) Less than or equal to GM
    d) None
    Answer: c) Less than or equal to GM
36. The sum of squares of first n natural numbers is:
    a) n(n+1)(2n+1)/6
    b) n(n+1)(2n–1)/6
    c) n²(n+1)²/4
    d) n(n+1)/2
    Answer: a) n(n+1)(2n+1)/6
37. The sum of cubes of first n natural numbers is:
    a) [n(n+1)/2]²
    b) n(n+1)(2n+1)/6
    c) n³/3
    d) n²(n+1)²
    Answer: a) [n(n+1)/2]²
38. The series 1 + 2 + 4 + 8 + … + 2ⁿ⁻¹ is a:
    a) AP
    b) GP
    c) HP
    d) None
    Answer: b) GP
39. If the nth term of a series is 2n – 1, the series is:
    a) Even natural numbers
    b) Odd natural numbers
    c) Prime numbers
    d) None
    Answer: b) Odd natural numbers
40. The sum of first 100 even natural numbers is:
    a) 10100
    b) 10000
    c) 5050
    d) 100100
    Answer: a) 10100
41. The 15th term from the end of AP: 7, 10, 13, …, 184 is:
    a) 145
    b) 148
    c) 150
    d) 155
    Answer: a) 145
42. If a, b, c are in AP, then (b–a), (c–b) are:
    a) Equal
    b) Unequal
    c) Dependent on a
    d) None
    Answer: a) Equal
43. The sum of infinite GP 5 + 2.5 + 1.25 + … is:
    a) 9
    b) 10
    c) 15
    d) 20
    Answer: b) 10
44. If the 5th term of a GP is 48 and common ratio is 2, the first term is:
    a) 2
    b) 3
    c) 4
    d) 1.5
    Answer: b) 3
45. In an AP, the 8th term is 17 and 15th term is 38. Then the common difference is:
    a) 3
    b) 2
    c) 5
    d) 7
    Answer: c) 3
46. The sum of first 20 terms of GP 1, 2, 4, … is:
    a) 2²⁰ – 1
    b) 2²⁰
    c) 2¹⁹ – 1
    d) 2¹⁹
    Answer: a) 2²⁰ – 1
47. The sequence sin x, sin 2x, sin 3x,… is:
    a) AP
    b) GP
    c) Neither AP nor GP
    d) HP
    Answer: c) Neither AP nor GP
48. If the sum of first n terms of an AP is proportional to n², then the AP is:
    a) Constant
    b) Increasing linearly
    c) Increasing quadratically
    d) None
    Answer: b) Increasing linearly
49. The geometric mean of 4 and 16 is:
    a) 6
    b) 8
    c) 10
    d) 12
    Answer: b) 8
50. The nth term of GP with a = 2, r = 5 is:
    a) 2(5ⁿ⁻¹)
    b) 5(2ⁿ⁻¹)
    c) 2ⁿ⁻¹(5)
    d) None
    Answer: a) 2(5ⁿ⁻¹)
51. Section J: Higher-Order Questions
52. If a, b, c are in AP, then 2b = ?
    a) a + c
    b) a – c
    c) c – a
    d) ac
    Answer: a) a + c
53. If a, b, c are in GP, then b² = ?
    a) ac
    b) a + c
    c) a – c
    d) None
    Answer: a) ac
54. If a, b, c are in HP, then 2/b = ?
    a) 1/a + 1/c
    b) a + c
    c) a – c
    d) None
    Answer: a) 1/a + 1/c
55. The sum of first 12 terms of AP: 11, 8, 5,… is:
    a) –54
    b) –24
    c) –14
    d) –34
    Answer: a) –54
56. The nth term of AP is 7 – 4n. Its 5th term is:
    a) –13
    b) –14
    c) –12
    d) –11
    Answer: b) –13
57. The sum of first n odd numbers is always:
    a) n²
    b) 2n
    c) n(n+1)
    d) n² – 1
    Answer: a) n²
58. If the sum of n terms is 2n² + 3n, then the first term is:
    a) 2
    b) 5
    c) 7
    d) 3
    Answer: b) 5
59. The sequence 1, 2, 4, 7, 11,… is:
    a) AP
    b) GP
    c) Neither AP nor GP
    d) HP
    Answer: c) Neither AP nor GP
60. The 10th term of sequence defined by an = 3n – 2 is:
    a) 28
    b) 25
    c) 30
    d) 27
    Answer: a) 28
61. If the sum of infinite GP is 12 and first term is 8, the common ratio is:
    a) ⅔
    b) ⅓
    c) ¼
    d) ½
    Answer: a) ⅔