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

A.P

G.P

A sequence

Not a sequence

2. 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

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

5/7

2/3

3/2

4. 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

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

± 3

± 9

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

122,144

112,288

None of these

108,188

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

y + 1

y – 1/y

y – 1

y – 1/2y

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

1/3

5/6

2/4

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

1/192

1/384

1/128

1/256

10. Three G.M between 5 & 0.008 are

0.02,0.05,0.06

1.0,2,0.0.04

02,0.5.0.6

None of these

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

-3

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

Arithmetic

None of these

Geometric

Harmonic

13. Common fraction of 7.755 is

349/45

3139/95

290/61

495/3839

14. 5th term of a G.P. is 2, then the product of first 9 terms is

128

256

None of these

512

15. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

117

146/2

124

119/2

17. 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 + n(b–a)/n+1

a + m(a–b)/n+1

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

√(5)

3√(5)

2√(5)

4√(5)

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

-13

-7

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

Harmonic series

G.P

A.P

H.P

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

None of these

G.P.

A.P.

H.P.

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

1,3,5,……

2,3,5,……

5,3,1,……

1,3,6,…..

23. Nth term of A.P is

a + nd

a + d/n

a + (n – 1)d

None of these

24. 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

25. An A.P. consists of n (odd terms) and its middle term is m. then the sum of the A.P. is

½ mn

mn²

2 mn

Page 2 of 4

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

a + (n – 1) d

a (1 – rⁿ)/1 – r

arⁿ¯¹

n/2 {2a + (n – 1) d}

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

14/15

56/15

112/15

28/15

28. 21 + 22 + 23 + …….. + 2n =

None of these

2(2n – 1)

2(2n + 1 – 1)

2(2n – 1 – 1)

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

6/5

–3/5

–4/9

5/3

30. 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)ⁿᐟⁿ⁺¹

a(b/a)ᵐᐟⁿ⁺¹

31. The A.M between 1 – x + x² is

1 + x²

1 – x²

2 – x²

2 + x²

32. Geometric sequence cannot contain

None of these

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

Common ratio

Geometric mean

Common difference

Arithmetic mean

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

A sequence

G.P

Not a sequence

A.P

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

64 and 4

2 and 64

None of these

64 and 3

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

Infinite series

Arithmetic series

Geometric series

Harmonic series

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

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

None of these

1,2,3, …………..

-2/3, 1, 7/3 ………….

-7/5, -5/3, -1,……..

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

√(2)

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

Geometric series

Infinite series

Arithmetic series

Harmonic series

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

-2/7

1/9

-5/6

-2

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

In A.P

In G.P

Real numbers

In H.P

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

– 2

– 1

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

a+b/2ab

2ab/(a+b)

2ab/a-b

a-b/2ab

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

Identity function

Sequence

Series

Onto function

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,

G.P,

A.P.,

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

A.P

H.P

G.P

Harmonic series

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

a+b/2ab

2ab/a+b

ab/a+b

a+b/2

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

– 1 ≤ r ≤ 1

r < – 1, r > 1

– 1 < r < 1

r ≤ – 1, r ≥ 1

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

–7

–13

Page 3 of 4

51. 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

52. 2¹+2²+2³+…+2ⁿ =

None of these

2(2ⁿ⁺¹ – 1)

2(2ⁿ – 1)

2(2ⁿ¯¹ – 1)

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

√2

54. No term of an harmonic sequence can be

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

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

± 1

± 3

± 2

± 4

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

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

(a–b)/2

(a+b)/2

a–b

a+b

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

A sequence

A.P

Not a sequence

G.P

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

Geometric series

Harmonic series

Infinite series

Arithmetic series

61. Which one is true?

H² = AG

G² = AH

A² = GH

None of these

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

-0.5

-1

-2

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

–1/3

– ½

1/3

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

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

-18

-324

None of these

324

66. 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

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

d – c

2 (f – d)

2 (d – c)

2 (c – a)

68. The common ratio of a geometric sequence cannot be

69. 2,4,6,8,10,12, ….. is

Geometric series

G.P

Arithmetic series

A.P

70. 4:32 can be written in

Binomial series

None of these

Infinite geometric series

Arithmetic series

71. 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

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

Arithmetic series

Infinite series

Harmonic series

Geometric series

73. 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

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

None of these

4⁵

4³

4⁶

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

Page 4 of 4

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

None of these

Divergent

Convergent

Oscillatory

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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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