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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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Math

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

Geometric series

Infinite series

Harmonic series

Arithmetic series

2. 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

3. 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

– 1 ≤ r ≤ 1

r ≤ – 1, r ≥ 1

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

108,188

112,288

None of these

122,144

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

½ mn

2 mn

mn²

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

1,3,6,…..

5,3,1,……

2,3,5,……

1,3,5,……

7. 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

None of these

xyz

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

-0.5

-2

-1

9. No term of an harmonic sequence can be

10. 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, a

n, b

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

Arithmetic series

Geometric series

Infinite series

Harmonic series

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

-2

1/9

-5/6

-2/7

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

G.P

None of these

H.P

A.P

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

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

± 3

± 9

16. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/256

1/128

1/192

1/384

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

A.P.

H.P.

G.P.

None of these

18. 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

H.P.

None of these

G.P.

A.P.

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

H.P,

G.P,

A.P.,

None of these

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

1,2,3, …………..

-2/3, 1, 7/3 ………….

-7/5, -5/3, -1,……..

None of these

21. 4:32 can be written in

Binomial series

Arithmetic series

None of these

Infinite geometric series

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

Onto function

Identity function

Series

Sequence

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

112/15

56/15

14/15

28/15

24. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

a-b/2ab

2ab/a-b

a+b/2ab

2ab/(a+b)

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

–13

–7

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

y – 1/2y

y – 1

y – 1/y

y + 1

28. 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

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

Harmonic series

G.P

H.P

A.P

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

G.P

A sequence

Not a sequence

A.P

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

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

– 1

– 2

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

None of these

Arithmetic

Harmonic

Geometric

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

124

146/2

119/2

117

35. Which one is true?

None of these

A² = GH

G² = AH

H² = AG

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

a+b/2

2ab/a+b

ab/a+b

a+b/2ab

37. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ¯¹ – 1)

2(2ⁿ – 1)

None of these

2(2ⁿ⁺¹ – 1)

38. 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 H.P

Real numbers

In A.P

39. 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

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

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

Infinite series

Harmonic series

Arithmetic series

Geometric series

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

3/2

2/3

5/7

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

17, 3n – 4

17, 4n – 3

4n – 3, 17

17, 4n

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

√2

45. Geometric sequence cannot contain

None of these

46. Three G.M between 5 & 0.008 are

None of these

1.0,2,0.0.04

02,0.5.0.6

0.02,0.05,0.06

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

None of these

324

-324

-18

48. The common ratio of a geometric sequence cannot be

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

1/3

– ½

–1/3

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

a (1 – rⁿ)/1 – r

n/2 {2a + (n – 1) d}

arⁿ¯¹

a + (n – 1) d

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

–4/9

–3/5

6/5

5/3

52. 21 + 22 + 23 + …….. + 2n =

2(2n + 1 – 1)

None of these

2(2n – 1 – 1)

2(2n – 1)

53. The A.M between 1 – x + x² is

1 – x²

2 – x²

1 + x²

2 + x²

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

A.P

A sequence

G.P

Not a sequence

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

2/4

5/6

1/3

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

G.P

A.P

H.P

Harmonic series

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

± 4

± 2

± 3

± 1

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

2 (c – a)

2 (f – d)

2 (d – c)

d – c

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

-13

-7

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

Oscillatory

Convergent

Divergent

None of these

61. Nth term of A.P is

a + (n – 1)d

a + nd

a + d/n

None of these

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

√(5)

2√(5)

3√(5)

4√(5)

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

64 and 4

2 and 64

64 and 3

None of these

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

Infinite series

Geometric series

Harmonic series

Arithmetic series

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

Common ratio

Geometric mean

Arithmetic mean

Common difference

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

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

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

None of these

4³

4⁶

4⁵

69. 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(a–b)/n+1

a + m(b–a)/n+1

a + n(b–a)/n+1

None of these

70. 2,4,6,8,10,12, ….. is

A.P

G.P

Geometric series

Arithmetic series

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

√(2)

72. 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

A sequence

G.P

73. Common fraction of 7.755 is

3139/95

290/61

495/3839

349/45

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

(a+b)/2

a–b

a+b

(a–b)/2

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

-3

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76. 5th term of a G.P. is 2, then the product of first 9 terms is

256

128

None of these

512

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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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