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

3/2

5/7

2/3

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

H.P

A.P

None of these

G.P

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

2ab/a+b

a+b/2

ab/a+b

a+b/2ab

4. 2,4,6,8,10,12, ….. is

Arithmetic series

Geometric series

A.P

G.P

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

5,3,1,……

1,3,6,…..

2,3,5,……

1,3,5,……

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

None of these

-324

-18

324

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

8. 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

In G.P

Real numbers

9. Which one is true?

G² = AH

A² = GH

H² = AG

None of these

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

± 3

± 1

± 2

± 4

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

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

a (1 – rⁿ)/1 – r

arⁿ¯¹

n/2 {2a + (n – 1) d}

a + (n – 1) d

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

–4/9

6/5

5/3

–3/5

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

Geometric series

Harmonic series

Arithmetic series

Infinite series

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

Convergent

None of these

Divergent

Oscillatory

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

1/128

1/192

1/256

1/384

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

H.P

A.P

G.P

Harmonic series

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

A.P.,

G.P,

H.P,

None of these

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

-2/7

1/9

-5/6

-2

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

– 2

– 1

21. 4:32 can be written in

Arithmetic series

None of these

Binomial series

Infinite geometric series

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

Arithmetic mean

Common difference

Geometric mean

Common ratio

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

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

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

112/15

14/15

56/15

28/15

Page 2 of 4

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

Harmonic series

Geometric series

Arithmetic series

Infinite series

27. 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

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

A sequence

G.P

A.P

Not a sequence

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

30. The A.M between 1 – x + x² is

2 + x²

1 – x²

2 – x²

1 + x²

31. 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

32. 21 + 22 + 23 + …….. + 2n =

2(2n – 1)

None of these

2(2n + 1 – 1)

2(2n – 1 – 1)

33. Nth term of A.P is

None of these

a + (n – 1)d

a + d/n

a + nd

34. 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

35. 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

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

(a+b)/2

(a–b)/2

a–b

a+b

37. 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.

None of these

H.P.

A.P.

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

√2

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

1/3

–1/3

– ½

40. The common ratio of a geometric sequence cannot be

41. 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

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

-3

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

H.P.

G.P.

A.P.

None of these

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

-1

-2

-0.5

45. Geometric sequence cannot contain

None of these

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

y + 1

y – 1/2y

y – 1/y

y – 1

47. 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

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

117

146/2

124

119/2

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

-7

-13

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

64 and 4

None of these

2 and 64

64 and 3

Page 3 of 4

51. Three G.M between 5 & 0.008 are

1.0,2,0.0.04

02,0.5.0.6

None of these

0.02,0.05,0.06

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

Infinite series

Arithmetic series

Geometric series

Harmonic series

53. 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

None of these

a + n(b–a)/n+1

54. 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

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

A.P

G.P

Not a sequence

A sequence

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

2/4

5/6

1/3

57. 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.P

A sequence

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

√(2)

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

Arithmetic series

Harmonic series

Geometric series

Infinite series

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

None of these

-7/5, -5/3, -1,……..

1,2,3, …………..

-2/3, 1, 7/3 ………….

61. Common fraction of 7.755 is

349/45

290/61

3139/95

495/3839

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

122,144

108,188

None of these

112,288

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

4⁶

4³

4⁵

None of these

64. 5th term of a G.P. is 2, then the product of first 9 terms is

128

None of these

512

256

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

Sequence

Series

Identity function

Onto function

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

2√(5)

3√(5)

√(5)

4√(5)

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

4n – 3, 17

17, 4n – 3

17, 4n

17, 3n – 4

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

a-b/2ab

a+b/2ab

2ab/(a+b)

2ab/a-b

69. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

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

Arithmetic

None of these

Harmonic

Geometric

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

± 9

± 3

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

H.P

A.P

Harmonic series

G.P

73. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ⁺¹ – 1)

None of these

2(2ⁿ¯¹ – 1)

2(2ⁿ – 1)

74. If a, r and an are the first term, common ratio and nth term respectively of the G.P, then an =

arⁿ

arⁿ¯¹

arⁿ⁺¹

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

–13

–7

Page 4 of 4

76. No term of an harmonic sequence can be

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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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