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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

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Page 1 of 4

Math

1. 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.

G.P.

None of these

A.P.

2. The common ratio of a geometric sequence cannot be

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

324

None of these

-324

-18

4. Common fraction of 7.755 is

495/3839

349/45

290/61

3139/95

5. 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

6. 4:32 can be written in

Arithmetic series

Binomial series

None of these

Infinite geometric series

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

y – 1/2y

y – 1/y

y + 1

y – 1

8. 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

G.P

A sequence

9. 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

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

a+b

(a+b)/2

a–b

(a–b)/2

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

-0.5

-2

-1

12. No term of an harmonic sequence can be

13. 21 + 22 + 23 + …….. + 2n =

2(2n + 1 – 1)

2(2n – 1)

None of these

2(2n – 1 – 1)

14. 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

15. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

-13

-7

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

A.P

Not a sequence

G.P

A sequence

18. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/384

1/192

1/256

19. Three G.M between 5 & 0.008 are

0.02,0.05,0.06

None of these

1.0,2,0.0.04

02,0.5.0.6

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

–7

–13

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

Series

Identity function

Sequence

Onto function

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

Not a sequence

G.P

A sequence

A.P

23. 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

a + m(b–a)/n+1

a + m(a–b)/n+1

None of these

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

2 (c – a)

2 (f – d)

d – c

2 (d – c)

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

± 3

± 9

Page 2 of 4

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

5,3,1,……

1,3,5,……

1,3,6,…..

2,3,5,……

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

28. 2¹+2²+2³+…+2ⁿ =

None of these

2(2ⁿ⁺¹ – 1)

2(2ⁿ¯¹ – 1)

2(2ⁿ – 1)

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

-2

1/9

-2/7

-5/6

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

None of these

Geometric

Arithmetic

Harmonic

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

2ab/(a+b)

a+b/2ab

2ab/a-b

a-b/2ab

32. 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,……..

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

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

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

Harmonic series

Arithmetic series

Infinite series

Geometric series

36. 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

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

Arithmetic mean

Geometric mean

Common difference

Common ratio

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

None of these

Convergent

Oscillatory

Divergent

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

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

Arithmetic series

Geometric series

Harmonic series

Infinite series

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

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

G.P.

None of these

A.P.

H.P.

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

2/4

1/3

5/6

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

– 1

– 2

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

√(5)

3√(5)

2√(5)

4√(5)

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

14/15

56/15

112/15

28/15

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

√(2)

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

5/7

3/2

2/3

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

64 and 3

64 and 4

None of these

2 and 64

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

H.P

Harmonic series

G.P

A.P

Page 3 of 4

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

± 1

± 2

± 4

± 3

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

In H.P

In A.P

Real numbers

In G.P

53. Which one is true?

H² = AG

A² = GH

None of these

G² = AH

54. 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

55. 5th term of a G.P. is 2, then the product of first 9 terms is

None of these

512

256

128

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

1/3

– ½

–1/3

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

Arithmetic series

Infinite series

Geometric series

Harmonic series

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

119/2

117

124

146/2

59. 2,4,6,8,10,12, ….. is

G.P

A.P

Arithmetic series

Geometric series

60. 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

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

Arithmetic series

Harmonic series

Geometric series

Infinite series

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

None of these

112,288

108,188

122,144

63. 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

64. The A.M between 1 – x + x² is

2 + x²

1 + x²

2 – x²

1 – x²

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

-3

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

a (1 – rⁿ)/1 – r

arⁿ¯¹

a + (n – 1) d

n/2 {2a + (n – 1) d}

67. 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

68. Nth term of A.P is

None of these

a + d/n

a + nd

a + (n – 1)d

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

2ab/a+b

ab/a+b

a+b/2ab

a+b/2

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

√2

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

–3/5

5/3

–4/9

6/5

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

b(b/a)ᵐᐟⁿ⁺¹

A(b/a)ⁿᐟⁿ⁺¹

73. 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, b

n, a

74. Geometric sequence cannot contain

None of these

75. 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

Page 4 of 4

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

None of these

4⁶

4⁵

4³

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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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