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

ab/a+b

a+b/2ab

a+b/2

2ab/a+b

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

1/3

5/6

2/4

3. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ¯¹ – 1)

2(2ⁿ⁺¹ – 1)

2(2ⁿ – 1)

None of these

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

4³

None of these

4⁶

4⁵

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

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

1/9

-2/7

-5/6

-2

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

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

None of these

H.P

A.P

G.P

9. 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, a, b

n, b

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

Convergent

Oscillatory

Divergent

None of these

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

64 and 4

64 and 3

None of these

2 and 64

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

a+b

a–b

(a–b)/2

(a+b)/2

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

Geometric series

Arithmetic series

Infinite series

Harmonic series

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

Arithmetic series

Infinite series

Harmonic series

Geometric series

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

A.P

Not a sequence

A sequence

G.P

16. 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

17. The A.M between 1 – x + x² is

2 + x²

1 – x²

2 – x²

1 + x²

18. Which one is true?

None of these

H² = AG

A² = GH

G² = AH

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

5/3

–4/9

6/5

–3/5

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

–13

–7

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

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

None of these

-2/3, 1, 7/3 ………….

1,2,3, …………..

-7/5, -5/3, -1,……..

23. 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

24. 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 sequence

A.P

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

Geometric

Harmonic

Arithmetic

None of these

Page 2 of 4

26. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

Real numbers

In A.P

In G.P

In H.P

28. 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

A sequence

G.P

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

H.P

Harmonic series

G.P

A.P

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

None of these

324

-324

-18

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

√(2)

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

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

a-b/2ab

2ab/a-b

a+b/2ab

2ab/(a+b)

34. Geometric sequence cannot contain

None of these

35. 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

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

1/3

–1/3

– ½

37. 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

38. 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

39. 2,4,6,8,10,12, ….. is

A.P

Arithmetic series

G.P

Geometric series

40. 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.

G.P.

H.P.

None of these

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

1,3,5,……

2,3,5,……

1,3,6,…..

5,3,1,……

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

43. 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

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

n/2 {2a + (n – 1) d}

arⁿ¯¹

a (1 – rⁿ)/1 – r

a + (n – 1) d

45. 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

a(b/a)ᵐᐟⁿ⁺¹

b(b/a)ᵐᐟⁿ⁺¹

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

Common ratio

Common difference

Geometric mean

Arithmetic mean

47. Common fraction of 7.755 is

349/45

3139/95

290/61

495/3839

48. 21 + 22 + 23 + …….. + 2n =

None of these

2(2n + 1 – 1)

2(2n – 1)

2(2n – 1 – 1)

49. 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

None of these

a + m(a–b)/n+1

a + n(b–a)/n+1

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

146/2

119/2

117

124

Page 3 of 4

51. 4:32 can be written in

Infinite geometric series

Arithmetic series

None of these

Binomial series

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

Arithmetic series

Infinite series

Geometric series

Harmonic series

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

None of these

H.P.

A.P.

G.P.

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

5/7

2/3

3/2

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

d – c

2 (d – c)

2 (c – a)

2 (f – d)

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

Harmonic series

H.P

G.P

A.P

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

– 2

– 1

58. 5th term of a G.P. is 2, then the product of first 9 terms is

None of these

128

512

256

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

112/15

14/15

28/15

56/15

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

-3

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

-0.5

-1

-2

62. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/192

1/384

1/256

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

4√(5)

3√(5)

2√(5)

√(5)

64. No term of an harmonic sequence can be

65. 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

66. The common ratio of a geometric sequence cannot be

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

Arithmetic series

Infinite series

Geometric series

Harmonic series

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

Sequence

Identity function

Onto function

Series

69. 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

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

√2

71. Nth term of A.P is

a + nd

a + d/n

a + (n – 1)d

None of these

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

± 2

± 3

± 4

± 1

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

y – 1/2y

y – 1/y

y – 1

y + 1

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

122,144

112,288

None of these

108,188

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

-13

-7

Page 4 of 4

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

± 3

± 9

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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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Maan Ali

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