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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, b, c are in AP, then 1/a, 1/b, 1/c are in

A.P

G.P

None of these

H.P

2. The A.M between 1 – x + x² is

2 + x²

1 + x²

1 – x²

2 – x²

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

-18

None of these

-324

324

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

± 4

± 2

± 1

± 3

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

-3

6. 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

G.P.

A.P.

H.P.

7. The common ratio of a geometric sequence cannot be

8. 21 + 22 + 23 + …….. + 2n =

2(2n – 1)

2(2n + 1 – 1)

None of these

2(2n – 1 – 1)

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

4³

None of these

4⁵

4⁶

10. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/192

1/256

1/384

1/128

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

a + (n – 1) d

n/2 {2a + (n – 1) d}

arⁿ¯¹

a (1 – rⁿ)/1 – r

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

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

G.P

A.P

Harmonic series

H.P

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

G.P

A sequence

Not a sequence

A.P

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

64 and 4

None of these

2 and 64

64 and 3

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

2√(5)

3√(5)

√(5)

4√(5)

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

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

-5/6

-2

-2/7

1/9

19. 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

r < – 1, r > 1

– 1 < r < 1

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

Harmonic

None of these

Geometric

Arithmetic

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

117

146/2

124

119/2

22. 4:32 can be written in

Infinite geometric series

Arithmetic series

None of these

Binomial series

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

–1/3

1/3

– ½

24. 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

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

± 9

± 3

Page 2 of 4

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

1,2,3, …………..

-2/3, 1, 7/3 ………….

None of these

-7/5, -5/3, -1,……..

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

-7

-13

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

A sequence

Not a sequence

A.P

G.P

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

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

None of these

Oscillatory

Divergent

Convergent

31. Nth term of A.P is

a + (n – 1)d

a + d/n

None of these

a + nd

32. 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 A.P

In G.P

33. Geometric sequence cannot contain

None of these

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

Geometric mean

Arithmetic mean

Common difference

Common ratio

35. 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

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

Onto function

Identity function

Series

Sequence

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

√(2)

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

–13

–7

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

– 1

– 2

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

a+b/2ab

a+b/2

2ab/a+b

ab/a+b

41. 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

42. 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

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

d – c

2 (d – c)

2 (f – d)

2 (c – a)

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

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

5/7

2/3

3/2

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

14/15

112/15

28/15

56/15

47. 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 + m(a–b)/n+1

a + n(b–a)/n+1

48. No term of an harmonic sequence can be

49. 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

G.P

A.P

50. 2,4,6,8,10,12, ….. is

Geometric series

Arithmetic series

G.P

A.P

Page 3 of 4

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

5/6

1/3

2/4

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

Infinite series

Harmonic series

Geometric series

Arithmetic series

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

-0.5

-1

-2

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

(a+b)/2

a–b

a+b

(a–b)/2

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

Harmonic series

Infinite series

Arithmetic series

Geometric series

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

17, 3n – 4

17, 4n

4n – 3, 17

17, 4n – 3

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

1,3,5,……

2,3,5,……

1,3,6,…..

5,3,1,……

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

√2

59. 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

60. 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

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

Harmonic series

G.P

H.P

A.P

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

–3/5

5/3

6/5

–4/9

63. Which one is true?

H² = AG

A² = GH

G² = AH

None of these

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

Geometric series

Arithmetic series

Infinite series

Harmonic series

65. 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

66. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ⁺¹ – 1)

None of these

2(2ⁿ – 1)

2(2ⁿ¯¹ – 1)

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

2ab/a-b

2ab/(a+b)

a-b/2ab

a+b/2ab

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

69. 5th term of a G.P. is 2, then the product of first 9 terms is

128

256

512

None of these

70. Common fraction of 7.755 is

495/3839

349/45

3139/95

290/61

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

None of these

122,144

112,288

108,188

72. 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

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

y – 1/2y

y – 1/y

y + 1

y – 1

74. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

a(b/a)¹ᐟ², b

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

Arithmetic series

Infinite series

Geometric series

Harmonic series

Page 4 of 4

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

A.P.

H.P.

None of these

G.P.

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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

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