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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. Nth term of A.P is

a + nd

a + (n – 1)d

a + d/n

None of these

2. 21 + 22 + 23 + …….. + 2n =

2(2n + 1 – 1)

None of these

2(2n – 1 – 1)

2(2n – 1)

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

Arithmetic

Geometric

None of these

Harmonic

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

Harmonic series

Geometric series

Arithmetic series

Infinite series

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

-2/7

-2

-5/6

1/9

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

3/2

2/3

5/7

7. 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

Not a sequence

A sequence

8. 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

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

56/15

28/15

112/15

14/15

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

324

-324

None of these

-18

11. 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

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

Infinite series

Harmonic series

Arithmetic series

Geometric series

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

A.P

H.P

None of these

G.P

14. No term of an harmonic sequence can be

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

± 4

± 2

± 3

± 1

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

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

18. Geometric sequence cannot contain

None of these

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

–4/9

–3/5

6/5

5/3

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

17, 4n – 3

4n – 3, 17

17, 3n – 4

17, 4n

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

Harmonic series

G.P

A.P

H.P

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

√2

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

– 2

– 1

24. Which one is true?

None of these

G² = AH

H² = AG

A² = GH

25. 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 G.P

In A.P

Page 2 of 4

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

-0.5

-1

-2

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

–1/3

1/3

– ½

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

(a–b)/2

a+b

(a+b)/2

a–b

29. 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

None of these

a + m(a–b)/n+1

a + m(b–a)/n+1

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

a + (n – 1) d

n/2 {2a + (n – 1) d}

a (1 – rⁿ)/1 – r

arⁿ¯¹

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

64 and 3

64 and 4

2 and 64

None of these

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

Convergent

Divergent

None of these

Oscillatory

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

–13

–7

34. 4:32 can be written in

Infinite geometric series

None of these

Binomial series

Arithmetic series

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

-2/3, 1, 7/3 ………….

-7/5, -5/3, -1,……..

1,2,3, …………..

None of these

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

A.P

A sequence

G.P

Not a sequence

37. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/192

1/384

1/256

38. 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.

None of these

H.P.

G.P.

39. The A.M between 1 – x + x² is

2 + x²

2 – x²

1 – x²

1 + x²

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

√(2)

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

-13

-7

42. 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.,

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

a+b/2

a+b/2ab

ab/a+b

2ab/a+b

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

Not a sequence

A sequence

G.P

A.P

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

2 mn

½ mn

mn²

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

√(5)

3√(5)

2√(5)

4√(5)

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

4³

4⁶

None of these

4⁵

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

5,3,1,……

1,3,5,……

1,3,6,…..

2,3,5,……

49. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ – 1)

2(2ⁿ¯¹ – 1)

None of these

2(2ⁿ⁺¹ – 1)

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

r ≤ – 1, r ≥ 1

r < – 1, r > 1

– 1 ≤ r ≤ 1

– 1 < r < 1

Page 3 of 4

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

Geometric series

Infinite series

Harmonic series

Arithmetic series

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

53. 5th term of a G.P. is 2, then the product of first 9 terms is

None of these

256

512

128

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

Arithmetic series

Geometric series

Harmonic series

Infinite series

55. 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

56. 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

G.P

Harmonic series

57. The two geometric means between a and b are

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

58. 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

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

G.P.

A.P.

H.P.

None of these

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

2 (d – c)

2 (c – a)

d – c

2 (f – d)

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

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

a+b/2ab

a-b/2ab

2ab/(a+b)

2ab/a-b

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

Series

Onto function

Identity function

Sequence

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

-3

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

112,288

None of these

122,144

108,188

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

y + 1

y – 1

y – 1/2y

y – 1/y

67. Common fraction of 7.755 is

290/61

495/3839

3139/95

349/45

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

2/4

1/3

5/6

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

± 9

± 3

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

Common ratio

Arithmetic mean

Common difference

Geometric mean

71. 2,4,6,8,10,12, ….. is

A.P

Geometric series

G.P

Arithmetic series

72. 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

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

74. Three G.M between 5 & 0.008 are

0.02,0.05,0.06

None of these

02,0.5.0.6

1.0,2,0.0.04

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

146/2

117

119/2

124

Page 4 of 4

76. The common ratio of a geometric sequence cannot 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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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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