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

½ mn

2 mn

mn²

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

√(2)

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

-0.5

-2

-1

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

Harmonic series

H.P

G.P

A.P

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

G.P

Not a sequence

A.P

A sequence

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

5/3

6/5

–3/5

–4/9

7. Geometric sequence cannot contain

None of these

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

arⁿ¯¹

a + (n – 1) d

a (1 – rⁿ)/1 – r

n/2 {2a + (n – 1) d}

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

112,288

None of these

122,144

108,188

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

y – 1

y – 1/y

y – 1/2y

y + 1

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

G.P

Not a sequence

A.P

A sequence

12. 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

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

Infinite series

Geometric series

Harmonic series

Arithmetic series

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

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

-13

-7

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

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

Arithmetic mean

Common ratio

Common difference

Geometric mean

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

± 9

± 3

19. Nth term of A.P is

None of these

a + d/n

a + (n – 1)d

a + nd

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

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

None of these

A.P.

G.P.

H.P.

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

a+b

(a–b)/2

(a+b)/2

a–b

23. 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.

24. 4:32 can be written in

Binomial series

None of these

Infinite geometric series

Arithmetic series

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

Page 2 of 4

26. 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

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

Geometric series

Infinite series

Harmonic series

Arithmetic series

28. 5th term of a G.P. is 2, then the product of first 9 terms is

128

None of these

256

512

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

√2

30. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/256

1/384

1/128

1/192

31. The common ratio of a geometric sequence cannot be

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

64 and 3

64 and 4

None of these

2 and 64

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

1,2,3, …………..

-2/3, 1, 7/3 ………….

-7/5, -5/3, -1,……..

None of these

34. 21 + 22 + 23 + …….. + 2n =

None of these

2(2n – 1)

2(2n – 1 – 1)

2(2n + 1 – 1)

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. No term of an harmonic sequence can be

37. 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(a–b)/n+1

a + m(b–a)/n+1

None of these

38. 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

39. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ¯¹ – 1)

None of these

2(2ⁿ – 1)

2(2ⁿ⁺¹ – 1)

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

41. Which one is true?

H² = AG

A² = GH

None of these

G² = AH

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

ab/a+b

2ab/a+b

a+b/2ab

a+b/2

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

4³

4⁶

4⁵

None of these

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

2 (c – a)

d – c

2 (d – c)

2 (f – d)

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

-5/6

-2

-2/7

1/9

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

-3

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

Onto function

Sequence

Series

Identity function

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

H.P,

A.P.,

None of these

G.P,

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

5,3,1,……

2,3,5,……

1,3,5,……

1,3,6,…..

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

119/2

124

146/2

117

Page 3 of 4

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

± 2

± 1

± 3

± 4

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

4√(5)

3√(5)

2√(5)

√(5)

53. Common fraction of 7.755 is

349/45

290/61

3139/95

495/3839

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

– ½

1/3

–1/3

55. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

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

Oscillatory

Divergent

None of these

Convergent

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

2ab/(a+b)

a-b/2ab

a+b/2ab

2ab/a-b

58. Three G.M between 5 & 0.008 are

None of these

0.02,0.05,0.06

1.0,2,0.0.04

02,0.5.0.6

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

Arithmetic

Harmonic

Geometric

None of these

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

112/15

56/15

28/15

14/15

61. 2,4,6,8,10,12, ….. is

A.P

G.P

Geometric series

Arithmetic series

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

– 1

– 2

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

G.P

H.P

None of these

A.P

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

A sequence

Not a sequence

G.P

A.P

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

-18

None of these

324

-324

66. 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 H.P

In G.P

67. The A.M between 1 – x + x² is

2 + x²

1 – x²

2 – x²

1 + x²

68. 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

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

2/4

5/6

1/3

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

–7

–13

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

17, 4n

17, 4n – 3

4n – 3, 17

17, 3n – 4

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

Harmonic series

Infinite series

Arithmetic series

Geometric series

73. 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

74. 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

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

G.P

Harmonic series

A.P

H.P

Page 4 of 4

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

Geometric series

Infinite series

Harmonic series

Arithmetic series

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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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