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

arⁿ¯¹

a (1 – rⁿ)/1 – r

a + (n – 1) d

n/2 {2a + (n – 1) d}

3. 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

4. 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

A.P

G.P

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

17, 4n

17, 4n – 3

17, 3n – 4

4n – 3, 17

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

± 3

± 9

7. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

8. 21 + 22 + 23 + …….. + 2n =

2(2n + 1 – 1)

None of these

2(2n – 1 – 1)

2(2n – 1)

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

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

Geometric

None of these

Arithmetic

Harmonic

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

12. 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

13. 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

14. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ – 1)

2(2ⁿ⁺¹ – 1)

2(2ⁿ¯¹ – 1)

None of these

15. 4:32 can be written in

Binomial series

None of these

Arithmetic series

Infinite geometric series

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

-324

None of these

-18

324

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

H.P

Harmonic series

G.P

A.P

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

3/2

2/3

5/7

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

H.P

G.P

A.P

Harmonic series

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

14/15

56/15

28/15

112/15

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

2,3,5,……

5,3,1,……

1,3,6,…..

1,3,5,……

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

2 (d – c)

2 (c – a)

2 (f – d)

d – c

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

Not a sequence

A sequence

A.P

G.P

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

Geometric series

Infinite series

Arithmetic series

Harmonic series

Page 2 of 4

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

Convergent

Oscillatory

Divergent

None of these

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

–1/3

– ½

1/3

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

124

119/2

146/2

117

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

In A.P

Real numbers

In G.P

In H.P

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

– 2

– 1

31. Common fraction of 7.755 is

3139/95

349/45

290/61

495/3839

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

Geometric series

Arithmetic series

Infinite series

Harmonic series

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

-13

-7

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

Geometric series

Arithmetic series

Infinite series

Harmonic series

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

Infinite series

Arithmetic series

Harmonic series

Geometric series

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

Arithmetic mean

Common ratio

Geometric mean

Common difference

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

± 4

± 1

± 3

± 2

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

a–b

a+b

(a–b)/2

(a+b)/2

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

5/6

2/4

1/3

40. 2,4,6,8,10,12, ….. is

Geometric series

G.P

Arithmetic series

A.P

41. Three G.M between 5 & 0.008 are

None of these

1.0,2,0.0.04

0.02,0.05,0.06

02,0.5.0.6

42. The A.M between 1 – x + x² is

1 – x²

2 + x²

1 + x²

2 – x²

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

mn²

½ mn

2 mn

44. 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

45. 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

a + m(a–b)/n+1

a + n(b–a)/n+1

None of these

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

-3

47. 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

48. 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

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

G.P.

H.P.

None of these

A.P.

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

-2

-2/7

1/9

-5/6

Page 3 of 4

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

–4/9

6/5

5/3

–3/5

52. 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

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

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

-2

-0.5

-1

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

√(2)

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

a+b/2ab

2ab/(a+b)

2ab/a-b

a-b/2ab

57. 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

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

4√(5)

2√(5)

3√(5)

√(5)

59. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/192

1/384

1/256

60. The common ratio of a geometric sequence cannot be

61. No term of an harmonic sequence can be

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

Onto function

Sequence

Series

Identity function

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

None of these

112,288

122,144

108,188

64. 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

None of these

H.P.

A.P.

G.P.

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

-2/3, 1, 7/3 ………….

1,2,3, …………..

None of these

-7/5, -5/3, -1,……..

66. 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

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

y + 1

y – 1/y

y – 1/2y

y – 1

68. Which one is true?

H² = AG

G² = AH

None of these

A² = GH

69. 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

70. Geometric sequence cannot contain

None of these

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

√2

72. 5th term of a G.P. is 2, then the product of first 9 terms is

512

256

128

None of these

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

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

–13

–7

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

2ab/a+b

a+b/2

a+b/2ab

ab/a+b

Page 4 of 4

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

4⁵

4³

None of these

4⁶

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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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