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

arⁿ¯¹

arⁿ⁺¹

arⁿ

2. If n is the total number of arithmetic means between a and b. The formula of mth arithmetic mean between a and b is

None of these

a + m(b–a)/n+1

a + n(b–a)/n+1

a + m(a–b)/n+1

3. 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

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

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

5/6

2/4

1/3

6. Common fraction of 7.755 is

290/61

349/45

3139/95

495/3839

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

1,2,3, …………..

None of these

-7/5, -5/3, -1,……..

-2/3, 1, 7/3 ………….

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

A.P.,

None of these

H.P,

G.P,

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

√(2)

10. Nth term of A.P is

None of these

a + nd

a + (n – 1)d

a + d/n

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

-2

-0.5

-1

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

56/15

28/15

14/15

112/15

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

-2/7

1/9

-5/6

-2

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

y – 1/y

y – 1

y + 1

y – 1/2y

15. 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

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

A.P.

H.P.

G.P.

None of these

17. 5th term of a G.P. is 2, then the product of first 9 terms is

128

256

None of these

512

18. The common ratio of a geometric sequence cannot be

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

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

√2

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

± 9

± 3

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

Series

Identity function

Onto function

Sequence

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

H.P

Harmonic series

A.P

G.P

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

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

Geometric series

Arithmetic series

Infinite series

Harmonic series

Page 2 of 4

26. 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

27. 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.P

G.P

A sequence

28. 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

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

H.P

A.P

G.P

None of these

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

Not a sequence

G.P

A sequence

A.P

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

-13

-7

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

-3

33. No term of an harmonic sequence can be

34. 4:32 can be written in

Arithmetic series

Infinite geometric series

None of these

Binomial series

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

5/7

3/2

2/3

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

–13

–7

37. 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

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

(a+b)/2

a–b

a+b

(a–b)/2

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

G.P

H.P

A.P

Harmonic series

40. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/192

1/384

1/256

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

Common ratio

Arithmetic mean

Common difference

Geometric mean

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

± 2

± 1

± 3

± 4

43. 2¹+2²+2³+…+2ⁿ =

None of these

2(2ⁿ⁺¹ – 1)

2(2ⁿ – 1)

2(2ⁿ¯¹ – 1)

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

Harmonic series

Geometric series

Infinite series

Arithmetic series

45. Which one is true?

G² = AH

H² = AG

A² = GH

None of these

46. 2,4,6,8,10,12, ….. is

G.P

Arithmetic series

A.P

Geometric series

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

2ab/(a+b)

a-b/2ab

2ab/a-b

a+b/2ab

48. 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

A.P.

H.P.

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

Arithmetic series

Geometric series

Infinite series

Harmonic series

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

None of these

4⁵

4⁶

4³

Page 3 of 4

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

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

A.P

Not a sequence

A sequence

G.P

53. 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

– 1 < r < 1

r < – 1, r > 1

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

Arithmetic

None of these

Harmonic

Geometric

55. 21 + 22 + 23 + …….. + 2n =

2(2n – 1 – 1)

None of these

2(2n – 1)

2(2n + 1 – 1)

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

1,3,5,……

1,3,6,…..

2,3,5,……

5,3,1,……

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

124

146/2

117

119/2

58. 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

In H.P

Real numbers

59. 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

60. Geometric sequence cannot contain

None of these

61. The A.M between 1 – x + x² is

2 – x²

1 – x²

1 + x²

2 + x²

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

√(5)

2√(5)

3√(5)

4√(5)

63. 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

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

-18

324

-324

None of these

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

122,144

112,288

108,188

None of these

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

– 2

– 1

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

d – c

2 (c – a)

2 (f – d)

2 (d – c)

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

17, 4n – 3

4n – 3, 17

17, 4n

17, 3n – 4

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

– ½

1/3

–1/3

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

5/3

–3/5

–4/9

6/5

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

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

ab/a+b

a+b/2ab

2ab/a+b

a+b/2

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

Oscillatory

None of these

Divergent

Convergent

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

Arithmetic series

Harmonic series

Infinite series

Geometric series

75. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

Page 4 of 4

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

64 and 4

64 and 3

2 and 64

None of these

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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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