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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Page 1 of 4

Math

1. 5th term of a G.P. is 2, then the product of first 9 terms is

512

256

None of these

128

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

Oscillatory

Convergent

None of these

Divergent

3. 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)ⁿᐟⁿ⁺¹

b(b/a)ᵐᐟⁿ⁺¹

a(b/a)ᵐᐟⁿ⁺¹

4. 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

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

√2

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

√(2)

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

-2/3, 1, 7/3 ………….

1,2,3, …………..

-7/5, -5/3, -1,……..

None of these

8. Nth term of A.P is

None of these

a + (n – 1)d

a + nd

a + d/n

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

Harmonic series

Geometric series

Arithmetic series

Infinite series

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

Infinite series

Geometric series

Arithmetic series

Harmonic series

11. Which one is true?

A² = GH

G² = AH

None of these

H² = AG

12. 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

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

a+b/2ab

a-b/2ab

2ab/(a+b)

2ab/a-b

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

2ab/a+b

a+b/2ab

ab/a+b

a+b/2

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

6/5

–3/5

–4/9

5/3

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

3/2

5/7

2/3

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

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

-2

-0.5

-1

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

– 1 ≤ r ≤ 1

– 1 < r < 1

r < – 1, r > 1

r ≤ – 1, r ≥ 1

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

a + m(b–a)/n+1

a + n(b–a)/n+1

None of these

a + m(a–b)/n+1

21. Common fraction of 7.755 is

290/61

495/3839

349/45

3139/95

22. The A.M between 1 – x + x² is

1 + x²

1 – x²

2 – x²

2 + x²

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

In G.P

In A.P

In H.P

Real numbers

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

56/15

112/15

14/15

28/15

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

Harmonic

Arithmetic

Geometric

None of these

Page 2 of 4

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

2/4

5/6

1/3

27. 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

Harmonic series

H.P

28. Geometric sequence cannot contain

None of these

29. The common ratio of a geometric sequence cannot be

30. 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

31. 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

None of these

G.P.

H.P.

A.P.

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

G.P

Not a sequence

A.P

A sequence

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

Not a sequence

G.P

A.P

A sequence

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

2 mn

mn²

½ mn

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

G.P.

A.P.

H.P.

None of these

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

± 1

± 2

± 3

± 4

37. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

arⁿ¯¹

arⁿ

arⁿ⁺¹

39. 4:32 can be written in

Binomial series

Arithmetic series

None of these

Infinite geometric series

40. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/384

1/256

1/192

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

Arithmetic series

Harmonic series

Geometric series

Infinite series

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

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

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

2 and 64

64 and 3

None of these

64 and 4

45. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ⁺¹ – 1)

2(2ⁿ¯¹ – 1)

None of these

2(2ⁿ – 1)

46. 21 + 22 + 23 + …….. + 2n =

2(2n – 1 – 1)

2(2n – 1)

2(2n + 1 – 1)

None of these

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

4⁵

4⁶

4³

None of these

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

1/9

-2/7

-5/6

-2

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

A.P

None of these

G.P

H.P

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

y + 1

y – 1/2y

y – 1/y

y – 1

Page 3 of 4

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

a + (n – 1) d

arⁿ¯¹

n/2 {2a + (n – 1) d}

a (1 – rⁿ)/1 – r

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

A sequence

G.P

A.P

Not a sequence

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

17, 4n – 3

4n – 3, 17

17, 4n

17, 3n – 4

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

-18

-324

324

None of these

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

5,3,1,……

2,3,5,……

1,3,5,……

1,3,6,…..

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

-3

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

– 2

– 1

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

Sequence

Onto function

Series

Identity function

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

a+b

(a–b)/2

(a+b)/2

a–b

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

2 (c – a)

2 (d – c)

d – c

2 (f – d)

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

A.P.,

G.P,

None of these

H.P,

62. Three G.M between 5 & 0.008 are

1.0,2,0.0.04

0.02,0.05,0.06

02,0.5.0.6

None of these

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

3√(5)

√(5)

2√(5)

4√(5)

64. 2,4,6,8,10,12, ….. is

Geometric series

Arithmetic series

G.P

A.P

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

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

–7

–13

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

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

H.P

G.P

Harmonic series

A.P

69. No term of an harmonic sequence can be

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

None of these

112,288

108,188

122,144

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

-7

-13

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

–1/3

1/3

– ½

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

Common ratio

Common difference

Geometric mean

Arithmetic mean

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

Harmonic series

Geometric series

Infinite series

Arithmetic series

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

± 3

± 9

Page 4 of 4

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

119/2

146/2

117

124

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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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