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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
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Math Sequences and Series Practice Test Online With Explanation

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Page 1 of 4

Math

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

None of these

A.P

H.P

G.P

2. The A.M between 1 – x + x² is

1 – x²

2 + x²

1 + x²

2 – x²

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

y – 1/y

y – 1

y – 1/2y

y + 1

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

5/6

1/3

2/4

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

r < – 1, r > 1

– 1 ≤ r ≤ 1

r ≤ – 1, r ≥ 1

– 1 < r < 1

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

G.P,

A.P.,

H.P,

None of these

7. Three G.M between 5 & 0.008 are

0.02,0.05,0.06

02,0.5.0.6

1.0,2,0.0.04

None of these

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

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

Sequence

Onto function

Identity function

Series

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

In A.P

Real numbers

In G.P

In H.P

11. Which one is true?

G² = AH

None of these

H² = AG

A² = GH

12. 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

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

± 3

± 9

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

Infinite series

Harmonic series

Arithmetic series

Geometric series

15. Common fraction of 7.755 is

495/3839

349/45

3139/95

290/61

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

G.P

Harmonic series

A.P

H.P

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

√2

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

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

Not a sequence

A sequence

A.P

G.P

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

G.P.

H.P.

None of these

A.P.

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

-3

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

a (1 – rⁿ)/1 – r

a + (n – 1) d

n/2 {2a + (n – 1) d}

arⁿ¯¹

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

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

25. Geometric sequence cannot contain

None of these

Page 2 of 4

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

(a–b)/2

a–b

(a+b)/2

a+b

27. 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 + n(b–a)/n+1

None of these

a + m(b–a)/n+1

a + m(a–b)/n+1

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

4⁶

None of these

4³

4⁵

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

A sequence

A.P

Not a sequence

G.P

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

-7

-13

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

arⁿ⁺¹

arⁿ¯¹

arⁿ

32. 2¹+2²+2³+…+2ⁿ =

None of these

2(2ⁿ – 1)

2(2ⁿ⁺¹ – 1)

2(2ⁿ¯¹ – 1)

33. 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

G.P

A.P

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

ab/a+b

a+b/2ab

a+b/2

2ab/a+b

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

-324

324

-18

None of these

36. 21 + 22 + 23 + …….. + 2n =

2(2n – 1 – 1)

None of these

2(2n + 1 – 1)

2(2n – 1)

37. No term of an harmonic sequence can be

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

2 (f – d)

2 (c – a)

d – c

2 (d – c)

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

mn²

½ mn

2 mn

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

1/3

– ½

–1/3

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

-2

-1

-0.5

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

124

119/2

146/2

117

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

1,2,3, …………..

-7/5, -5/3, -1,……..

None of these

-2/3, 1, 7/3 ………….

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

17, 4n

4n – 3, 17

17, 4n – 3

17, 3n – 4

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

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

√(2)

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

2,3,5,……

5,3,1,……

1,3,6,…..

1,3,5,……

48. 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

A.P.

H.P.

G.P.

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

H.P

G.P

A.P

Harmonic series

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

√(5)

2√(5)

3√(5)

4√(5)

Page 3 of 4

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

– 2

– 1

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

Infinite series

Harmonic series

Arithmetic series

Geometric series

53. 2,4,6,8,10,12, ….. is

Arithmetic series

Geometric series

G.P

A.P

54. 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

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

± 4

± 3

± 1

± 2

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

Arithmetic series

Harmonic series

Infinite series

Geometric series

57. 4:32 can be written in

None of these

Arithmetic series

Binomial series

Infinite geometric series

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

Arithmetic mean

Common difference

Geometric mean

Common ratio

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

Harmonic series

Infinite series

Geometric series

Arithmetic series

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

108,188

None of these

122,144

112,288

61. 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

n, b

n, a, b

62. Nth term of A.P is

None of these

a + (n – 1)d

a + nd

a + d/n

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

–4/9

5/3

6/5

–3/5

64. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/384

1/192

1/256

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

1/9

-5/6

-2/7

-2

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

a+b/2ab

2ab/(a+b)

a-b/2ab

2ab/a-b

67. The common ratio of a geometric sequence cannot be

68. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

14/15

56/15

28/15

112/15

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

2/3

3/2

5/7

71. 5th term of a G.P. is 2, then the product of first 9 terms is

256

512

128

None of these

72. 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

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

–13

–7

74. 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

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

Harmonic

Arithmetic

None of these

Geometric

Page 4 of 4

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

Oscillatory

None of these

Divergent

Convergent

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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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