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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
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ECAT Math Sequences and Series Chapter Online Test

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Page 1 of 4

Math

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

1/256

1/384

1/192

1/128

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

5/7

3/2

2/3

3. Nth term of A.P is

None of these

a + nd

a + (n – 1)d

a + d/n

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

5. 2,4,6,8,10,12, ….. is

G.P

A.P

Arithmetic series

Geometric series

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

In H.P

Real numbers

In A.P

In G.P

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

8. 5th term of a G.P. is 2, then the product of first 9 terms is

128

None of these

512

256

9. Three G.M between 5 & 0.008 are

None of these

02,0.5.0.6

0.02,0.05,0.06

1.0,2,0.0.04

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

-3

11. Geometric sequence cannot contain

None of these

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

17, 4n – 3

17, 4n

17, 3n – 4

4n – 3, 17

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

Geometric mean

Common ratio

Arithmetic mean

Common difference

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

± 1

± 3

± 4

± 2

15. 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

16. 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

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

1,3,6,…..

2,3,5,……

5,3,1,……

1,3,5,……

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

± 9

± 3

19. 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

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

Harmonic series

H.P

A.P

G.P

21. 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

G.P.

A.P.

H.P.

None of these

22. 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

G.P,

H.P,

A.P.,

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

-2

-1

-0.5

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

Harmonic series

Arithmetic series

Infinite series

Geometric series

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

Series

Onto function

Identity function

Sequence

Page 2 of 4

26. 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

27. 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

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

None of these

-2/3, 1, 7/3 ………….

-7/5, -5/3, -1,……..

1,2,3, …………..

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

Geometric series

Harmonic series

Arithmetic series

Infinite series

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

5/6

1/3

2/4

31. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

32. 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

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

-13

-7

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

None of these

108,188

112,288

122,144

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

None of these

2 and 64

64 and 4

64 and 3

36. 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

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

n/2 {2a + (n – 1) d}

a + (n – 1) d

arⁿ¯¹

a (1 – rⁿ)/1 – r

38. 21 + 22 + 23 + …….. + 2n =

None of these

2(2n – 1 – 1)

2(2n – 1)

2(2n + 1 – 1)

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

-2

-5/6

1/9

-2/7

40. Which one is true?

None of these

H² = AG

A² = GH

G² = AH

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

Harmonic series

Arithmetic series

Geometric series

Infinite series

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

Oscillatory

Convergent

Divergent

None of these

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

G.P

A sequence

Not a sequence

A.P

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

3√(5)

4√(5)

√(5)

2√(5)

45. 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

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

G.P.

A.P.

H.P.

None of these

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

Not a sequence

A.P

G.P

A sequence

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

49. Common fraction of 7.755 is

495/3839

349/45

290/61

3139/95

50. The A.M between 1 – x + x² is

1 – x²

2 + x²

1 + x²

2 – x²

Page 3 of 4

51. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ⁺¹ – 1)

2(2ⁿ¯¹ – 1)

2(2ⁿ – 1)

None of these

52. The common ratio of a geometric sequence cannot be

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

a–b

(a–b)/2

a+b

(a+b)/2

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

Infinite series

Arithmetic series

Geometric series

Harmonic series

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

-18

-324

324

None of these

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

a+b/2ab

ab/a+b

a+b/2

2ab/a+b

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

Arithmetic

Geometric

None of these

Harmonic

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

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

14/15

56/15

28/15

112/15

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

√2

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

– ½

–1/3

1/3

62. 4:32 can be written in

None of these

Arithmetic series

Infinite geometric series

Binomial series

63. No term of an harmonic sequence can be

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

4³

4⁵

None of these

4⁶

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

–13

–7

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

–3/5

6/5

–4/9

5/3

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

H.P

Harmonic series

A.P

G.P

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

2 (d – c)

2 (f – d)

2 (c – a)

d – c

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

y – 1/2y

y – 1/y

y – 1

y + 1

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

G.P

None of these

A.P

H.P

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

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

146/2

119/2

124

117

73. 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

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

a-b/2ab

2ab/a-b

a+b/2ab

2ab/(a+b)

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

√(2)

Page 4 of 4

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

– 2

– 1

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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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