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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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Math

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

Infinite series

Harmonic series

Geometric series

Arithmetic series

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

4³

None of these

4⁶

4⁵

3. Which one is true?

H² = AG

None of these

G² = AH

A² = GH

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

Convergent

Divergent

None of these

Oscillatory

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

6. 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

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

14/15

28/15

56/15

112/15

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

H.P,

None of these

A.P.,

G.P,

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

Sequence

Onto function

Series

Identity function

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

Not a sequence

G.P

A sequence

A.P

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

y + 1

y – 1/y

y – 1

y – 1/2y

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

17, 4n

17, 3n – 4

4n – 3, 17

17, 4n – 3

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

-3

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

–13

–7

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

2 and 64

None of these

64 and 4

64 and 3

16. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

146/2

117

124

119/2

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

Common difference

Geometric mean

Arithmetic mean

Common ratio

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

-13

-7

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

2 (f – d)

2 (c – a)

2 (d – c)

d – c

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

–3/5

5/3

6/5

–4/9

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

5,3,1,……

1,3,5,……

2,3,5,……

1,3,6,…..

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

– 1 < r < 1

– 1 ≤ r ≤ 1

r < – 1, r > 1

r ≤ – 1, r ≥ 1

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

Geometric series

Harmonic series

Arithmetic series

Infinite series

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

± 1

± 2

± 3

± 4

Page 2 of 4

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

1/3

2/4

5/6

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

Real numbers

In H.P

In G.P

In A.P

28. 2¹+2²+2³+…+2ⁿ =

None of these

2(2ⁿ – 1)

2(2ⁿ⁺¹ – 1)

2(2ⁿ¯¹ – 1)

29. Three G.M between 5 & 0.008 are

1.0,2,0.0.04

None of these

02,0.5.0.6

0.02,0.05,0.06

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

None of these

122,144

108,188

112,288

31. 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

32. 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.P

G.P

A sequence

33. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/384

1/256

1/192

1/128

34. 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

a + m(b–a)/n+1

a + m(a–b)/n+1

None of these

35. 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

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

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

A.P

G.P

None of these

H.P

38. 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

39. 2,4,6,8,10,12, ….. is

Arithmetic series

A.P

G.P

Geometric series

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

-2

1/9

-5/6

-2/7

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

324

None of these

-18

-324

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

√(2)

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

2ab/(a+b)

a+b/2ab

a-b/2ab

2ab/a-b

44. 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

a(b/a)ᵐᐟⁿ⁺¹

b(b/a)ᵐᐟⁿ⁺¹

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

5/7

3/2

2/3

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

G.P

H.P

A.P

Harmonic series

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

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

A.P.

None of these

H.P.

G.P.

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

Geometric

None of these

Harmonic

Arithmetic

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

-0.5

-1

-2

Page 3 of 4

51. Nth term of A.P is

a + d/n

a + (n – 1)d

None of these

a + nd

52. 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

53. The A.M between 1 – x + x² is

2 + x²

2 – x²

1 + x²

1 – x²

54. Geometric sequence cannot contain

None of these

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

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

– ½

1/3

–1/3

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

Arithmetic series

Infinite series

Geometric series

Harmonic series

58. 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

59. No term of an harmonic sequence can be

60. 21 + 22 + 23 + …….. + 2n =

2(2n + 1 – 1)

2(2n – 1 – 1)

2(2n – 1)

None of these

61. Common fraction of 7.755 is

3139/95

349/45

290/61

495/3839

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

arⁿ¯¹

arⁿ

arⁿ⁺¹

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

64. The common ratio of a geometric sequence cannot be

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

– 2

– 1

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

√(5)

4√(5)

2√(5)

3√(5)

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

1,2,3, …………..

-7/5, -5/3, -1,……..

-2/3, 1, 7/3 ………….

None of these

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

(a–b)/2

a+b

a–b

(a+b)/2

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

2ab/a+b

a+b/2

a+b/2ab

ab/a+b

70. 5th term of a G.P. is 2, then the product of first 9 terms is

512

None of these

256

128

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

√2

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

None of these

A.P.

H.P.

G.P.

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

Infinite series

Harmonic series

Geometric series

Arithmetic series

74. 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

75. 4:32 can be written in

None of these

Arithmetic series

Binomial series

Infinite geometric series

Page 4 of 4

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

± 9

± 3

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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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