Mathematics Sequences and Series Online Test

Maan AliLast Updated: October 15, 2025

Important Math Sequences and Series Question and Answer

Total Questions:	76
Time Allowed:	40 Minutes
Total Marks:	76
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Sequences and Series Practice Test Online With Explanation

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Math

1. The general term of an A.P is [2/3]ⁿ¯³ the sequence is

-7/5, -5/3, -1,……..

None of these

1,2,3, …………..

-2/3, 1, 7/3 ………….

2. G.M between two numbers 4 and -81 is

-18

324

None of these

-324

3. The A.P. whose nth term is 2n – 1 is

5,3,1,……

1,3,5,……

1,3,6,…..

2,3,5,……

4. If |x| < 1 and y = x-x² + x³-x⁴ + ………….. ∞, then the value of x is

y/1–y

y/1+y

y–1/y

y+1/y

5. If a, b, c are in A.P., then 3ᵃ, 3ᵇ, 3ᶜ are in

None of these

A.P.

H.P.

G.P.

6. The common difference of the sequence 5,8,11,14,…. Is

7. The value of 9¹ᐟ³, 9¹ᐟ⁹,9¹ᐟ²⁷ ………. ∞ is

8. The harmonic mean between the two numbers a and b is

a-b/2ab

2ab/a-b

a+b/2ab

2ab/(a+b)

9. The arithmetic mean between 2 + ?(2) and 2-?(2) is

√(2)

10. 4:32 can be written in

Arithmetic series

Infinite geometric series

Binomial series

None of these

11. The fifth term of the sequence an = 2n – 3 is

–13

–7

12. A function whose domain is the set of natural numbers is called

Onto function

Identity function

Sequence

Series

13. The next two terms of the sequence 1,3,7,15,31,.........are

None of these

108,188

112,288

122,144

14. The term of a GP is -36 and common ration is – 1/3 then a₅ =?

5/3

–4/9

–3/5

6/5

15. aⁿ+bⁿ/aⁿ¯¹+bⁿ¯¹ is a G.M between a and b if n is

–1/3

1/3

– ½

16. Geometric sequence cannot contain

None of these

17. If y = 1 + 2x + 4x² + 8x³ + ……….. ∞ then x = ?

y – 1/2y

y – 1/y

y – 1

y + 1

18. The next term of the sequence 1, 2, 4, 7, 11, …….. is.

19. The third term of a G.P. is 4. The product of first five terms is

None of these

4³

4⁶

4⁵

20. The fifth term of the sequence an = 2n + 3 is

-7

-13

21. Nth term of A.P is

None of these

a + d/n

a + nd

a + (n – 1)d

22. H₁, H₂, ….. Hn are said to be n harmonic means between a and b if a, H₁, H₂, ……… Hn, b form

G.P

A.P

H.P

Harmonic series

23. Given two numbers a and b. Let A denote the single A.M. between these and S denote the sum of n A.M.’s between them. Then S/A depends upon

n, a, b

n, b

n, a

24. A number G is said to be the geometric mean between two numbers a and b of a,G,b is

A.P

A sequence

Not a sequence

G.P

25. The general term of the sequence a, ar, ar, ….is

arⁿ¯¹

n/2 {2a + (n – 1) d}

a + (n – 1) d

a (1 – rⁿ)/1 – r

Page 2 of 4

26. Common fraction of 7.755 is

290/61

349/45

495/3839

3139/95

27. The geometric mean between -2t and 8t are

± 2

± 4

± 1

± 3

28. A.M between two numbers a and b is given by

(a–b)/2

a+b

a–b

(a+b)/2

29. If A, G, H are the arithmetic, geometric and harmonic means between a and b respectively, then A, G, H are

Real numbers

In H.P

In A.P

In G.P

30. The 5th term of the G.P. 3,6,12, …… is

31. If aⁿ⁺²+bⁿ⁺²/aⁿ⁺¹ + bⁿ⁺¹ is the geometric mean between a and b, then n =

-1

-2

-0.5

32. Series obtained by adding the terms of an harmonic sequence is

A.P

G.P

H.P

Harmonic series

33. The geometric mean between √3 and √27 is

± 9

± 3

34. For an H.P 3/11, 6/31, 3/20, ………. , The common difference of the corresponding AP is

3/2

5/7

2/3

35. The series obtained by adding the terms of an arithmetic sequence is called the

Arithmetic series

Geometric series

Infinite series

Harmonic series

36. If a, r and an are the first term, common ratio and nth term respectively of the G.P, then an =

arⁿ

arⁿ⁺¹

arⁿ¯¹

37. 21 + 22 + 23 + …….. + 2n =

2(2n + 1 – 1)

None of these

2(2n – 1 – 1)

2(2n – 1)

38. Is the harmonic mean between and b, then n =

– 2

– 1

39. A sequence in which any term dividend by its immediate previous terms is called the

Geometric mean

Common difference

Arithmetic mean

Common ratio

40. If a, b, c, d, e, f are in A.P., then e – c is equal to

2 (f – d)

2 (c – a)

2 (d – c)

d – c

41. The A.M. of two numbers is 34 and G.M. is 16, the numbers are

2 and 64

64 and 3

64 and 4

None of these

42. 2,4,6,8,10,12, ….. is

A.P

Geometric series

Arithmetic series

G.P

43. If x, y, z are the pth, qth, rth terms of an A.P. and also of G.P, the xʸ¯ˣ, yˣ¯ˣ, zˣ¯ʸ equals

xyz

None of these

44. A sequence of nos. Whose reciprocal from an arithmetic sequence is called _________ sequence.

None of these

Harmonic

Arithmetic

Geometric

45. 5th term of a G.P. is 2, then the product of first 9 terms is

256

None of these

128

512

46. If n is the total number of geometric mean between a and b than the nth geometric mean between a and b is

a(b/a)ᵐᐟⁿ⁺¹

A(b/a)ⁿᐟⁿ⁺¹

b(b/a)ᵐᐟⁿ⁺¹

47. An A.P. consists of n (odd terms) and its middle term is m. then the sum of the A.P. is

mn²

2 mn

½ mn

48. If Sr denotes the sum of the first r terms of a G.P., then Sn, S₂n – Sn, S₃n – S₂n are in

None of these

G.P,

A.P.,

H.P,

49. H.M between two numbers ‘a’ and ‘b’ is given by

a+b/2

a+b/2ab

2ab/a+b

ab/a+b

50. The A.M between 3?(5) and 5?(5) is

√(5)

4√(5)

2√(5)

3√(5)

Page 3 of 4

51. If a, b, c are in AP, then 1/a, 1/b, 1/c are in

A.P

None of these

H.P

G.P

52. If p, q, r are in A.P., a is G.M. between p and q and b is G.M. between q and r, then a², q², b² are in

G.P.

None of these

H.P.

A.P.

53. Sum of all the terms in sequence, 5/6, 25/36, ---- ∞ is

2/4

5/6

1/3

54. The arithmetic mean between 2 + √2 and 2 – √2 is

√2

55. Which one is true?

G² = AH

A² = GH

None of these

H² = AG

56. The A.M between 1 – x + x² is

2 + x²

1 – x²

1 + x²

2 – x²

57. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/384

1/128

1/256

1/192

58. The series obtained by adding the term of arithmetic sequence is called

Infinite series

Harmonic series

Geometric series

Arithmetic series

59. The series obtained by adding the terms of geometric sequences is called

Infinite series

Geometric series

Harmonic series

Arithmetic series

60. Three G.M between 5 & 0.008 are

02,0.5.0.6

1.0,2,0.0.04

0.02,0.05,0.06

None of these

61. The sum of an infinite geometric series exist only if the condition on the common ratio r is

– 1 ≤ r ≤ 1

r < – 1, r > 1

r ≤ – 1, r ≥ 1

– 1 < r < 1

62. No term of an harmonic sequence can be

63. G₁,G₂, ….., Gn are said to b n geometric means between a and b if a, G₁, G₂, …….., Gn b is

A sequence

Not a sequence

A.P

G.P

64. The fifth term and the nth term of the A.P. 1,5……. Are

4n – 3, 17

17, 4n – 3

17, 3n – 4

17, 4n

65. For ¼, 2/5, 1, ----------- 6th term is

-2

-5/6

-2/7

1/9

66. The series obtained by adding the terms of a geometric sequence is

Infinite series

Harmonic series

Geometric series

Arithmetic series

67. A number A is said to be the arithmetic mean between two numbers a and b if a, A, b is

A.P

Not a sequence

G.P

A sequence

68. a₂₇ of 7, 23/2, 32/2, --------- is

124

117

119/2

146/2

69. The common difference of the sequence 5,8,11,14,…is

-3

70. If n is the total number of arithmetic means between a and b. The formula of mth arithmetic mean between a and b is

None of these

a + m(b–a)/n+1

a + m(a–b)/n+1

a + n(b–a)/n+1

71. The common ratio of a geometric sequence cannot be

72. Let Sn denote the sum of the first n terms of an A.P. If S₂n = 3 Sn, then S₃n : Sn is equal to

73. If H is harmonic mean between 7 and 8, then H/2 =

56/15

28/15

112/15

14/15

74. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ – 1)

None of these

2(2ⁿ¯¹ – 1)

2(2ⁿ⁺¹ – 1)

75. If r< -1 and r > 1 then the series is

Divergent

Convergent

Oscillatory

None of these

Page 4 of 4

76. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

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Maan AliLast Updated: October 15, 2025

Mathematics Sequences and Series Online Test

Important Math Sequences and Series Question and Answer

Math Sequences and Series Practice Test Online With Explanation

Math

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