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ECAT Mathematics Sequences and Series Online Test

Maan AliLast Updated: April 18, 2025

Mathematics Sequences and Series MCQS Online Test

ECAT Math Sequences and Series Chapter Online Test

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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ECAT Math Sequences and Series Chapter Online Test

Page 1 of 4

Math

1. 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

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

– 2

– 1

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

√(2)

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

2ab/a-b

a+b/2ab

a-b/2ab

2ab/(a+b)

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

14/15

28/15

112/15

56/15

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

Not a sequence

A.P

A sequence

G.P

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

Arithmetic series

Geometric series

Harmonic series

Infinite series

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

-3

9. a₂₇ of 7, 23/2, 32/2, --------- is

146/2

117

119/2

124

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

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

± 3

± 1

± 4

± 2

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

17, 3n – 4

17, 4n

4n – 3, 17

17, 4n – 3

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

Geometric

Arithmetic

None of these

Harmonic

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

A.P

G.P

H.P

None of these

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

–7

–13

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

1/9

-2/7

-5/6

-2

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

None of these

Oscillatory

Convergent

Divergent

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

b(b/a)ᵐᐟⁿ⁺¹

a(b/a)ᵐᐟⁿ⁺¹

A(b/a)ⁿᐟⁿ⁺¹

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

-324

324

-18

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 ………….

None of these

-7/5, -5/3, -1,……..

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

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

1/3

5/6

2/4

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

a+b

(a–b)/2

a–b

(a+b)/2

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

Arithmetic series

Harmonic series

Infinite series

Geometric series

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

Onto function

Sequence

Series

Identity function

Page 2 of 4

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

r < – 1, r > 1

r ≤ – 1, r ≥ 1

– 1 < r < 1

– 1 ≤ r ≤ 1

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

G.P

A sequence

Not a sequence

A.P

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

y – 1

y + 1

y – 1/y

y – 1/2y

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

Arithmetic series

Geometric series

Infinite series

Harmonic series

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

√2

31. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ⁺¹ – 1)

2(2ⁿ¯¹ – 1)

None of these

2(2ⁿ – 1)

32. Which one is true?

H² = AG

A² = GH

G² = AH

None of these

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

–3/5

5/3

–4/9

6/5

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

Real numbers

In G.P

In A.P

In H.P

35. Nth term of A.P is

None of these

a + d/n

a + (n – 1)d

a + nd

36. 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

37. 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, b

n, a

n, a, b

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

2√(5)

4√(5)

√(5)

3√(5)

39. 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

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

Infinite series

Harmonic series

Arithmetic series

Geometric series

41. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/384

1/256

1/128

1/192

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

43. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

44. 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 + n(b–a)/n+1

None of these

a + m(b–a)/n+1

45. Common fraction of 7.755 is

495/3839

290/61

349/45

3139/95

46. 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

H.P,

A.P.,

G.P,

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

4⁵

4³

None of these

4⁶

48. 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

49. 21 + 22 + 23 + …….. + 2n =

2(2n – 1 – 1)

None of these

2(2n + 1 – 1)

2(2n – 1)

50. The common ratio of a geometric sequence cannot be

Page 3 of 4

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

–1/3

– ½

1/3

52. 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

53. 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

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

108,188

None of these

112,288

122,144

55. 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

A.P.

H.P.

G.P.

None of these

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

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

H.P

G.P

A.P

Harmonic series

58. Geometric sequence cannot contain

None of these

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

d – c

2 (f – d)

2 (c – a)

2 (d – c)

60. 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.P

G.P

A sequence

61. No term of an harmonic sequence can be

62. 2,4,6,8,10,12, ….. is

G.P

Geometric series

Arithmetic series

A.P

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

± 9

± 3

64. The A.M between 1 – x + x² is

1 + x²

2 + x²

1 – x²

2 – x²

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

5/7

3/2

2/3

66. 5th term of a G.P. is 2, then the product of first 9 terms is

256

512

None of these

128

67. 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

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

5,3,1,……

1,3,5,……

2,3,5,……

1,3,6,…..

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

-7

-13

70. 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

71. 4:32 can be written in

None of these

Arithmetic series

Binomial series

Infinite geometric series

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

Common difference

Common ratio

Arithmetic mean

Geometric mean

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

-1

-0.5

-2

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

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

a+b/2ab

ab/a+b

2ab/a+b

a+b/2

Page 4 of 4

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

A.P.

G.P.

H.P.

None of these

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Maan AliLast Updated: April 18, 2025

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ECAT Mathematics Sequences and Series Online Test

Mathematics Sequences and Series MCQS Online Test

ECAT Math Sequences and Series Chapter Online Test

ECAT Math Sequences and Series Chapter Online Test

Math

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Maan Ali

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Mathematics Sequences and Series MCQS Online Test

ECAT Math Sequences and Series Chapter Online Test

ECAT Math Sequences and Series Chapter Online Test

Math

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