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

4n – 3, 17

17, 3n – 4

17, 4n – 3

17, 4n

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

Geometric series

Infinite series

Arithmetic series

Harmonic series

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

arⁿ¯¹

n/2 {2a + (n – 1) d}

a + (n – 1) d

a (1 – rⁿ)/1 – r

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

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

324

None of these

-324

-18

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

None of these

122,144

108,188

112,288

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

Harmonic series

Geometric series

Arithmetic series

Infinite series

8. 2,4,6,8,10,12, ….. is

A.P

Geometric series

G.P

Arithmetic series

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

2√(5)

√(5)

4√(5)

3√(5)

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

√(2)

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

-1

-2

-0.5

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

-2/7

-5/6

-2

1/9

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

H.P

G.P

None of these

A.P

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

A.P

G.P

A sequence

Not a sequence

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

-3

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

17. Which one is true?

G² = AH

None of these

A² = GH

H² = AG

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

y – 1

y + 1

y – 1/y

y – 1/2y

19. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

1/128

1/384

1/256

1/192

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

28/15

56/15

14/15

112/15

21. 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

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

Harmonic series

H.P

A.P

G.P

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

124

117

119/2

146/2

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

d – c

2 (d – c)

2 (c – a)

2 (f – d)

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

– ½

–1/3

1/3

Page 2 of 4

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

1,3,5,……

1,3,6,…..

2,3,5,……

5,3,1,……

27. 5th term of a G.P. is 2, then the product of first 9 terms is

512

128

None of these

256

28. 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

29. 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

30. Common fraction of 7.755 is

349/45

3139/95

495/3839

290/61

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

± 3

± 2

± 4

± 1

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

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

Geometric series

Arithmetic series

Infinite series

Harmonic series

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

Arithmetic

None of these

Geometric

Harmonic

35. 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, b

n, a

n, b

36. The two geometric means between a and b are

a(b/a)¹ᐟ², b

b(a/b)¹ᐟ², b

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

5/6

1/3

2/4

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

Sequence

Identity function

Series

Onto function

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

In G.P

In A.P

In H.P

Real numbers

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

41. 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

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

± 9

± 3

43. 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(a–b)/n+1

a + m(b–a)/n+1

a + n(b–a)/n+1

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

None of these

G.P,

A.P.,

H.P,

45. 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.

H.P.

None of these

G.P.

46. 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

47. 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

A.P

H.P

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

None of these

Oscillatory

Divergent

Convergent

49. The A.M between 1 – x + x² is

1 + x²

2 + x²

1 – x²

2 – x²

50. 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

Page 3 of 4

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

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

xyz

None of these

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

√2

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

–13

–7

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

5/7

3/2

2/3

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

None of these

G.P.

A.P.

H.P.

57. Nth term of A.P is

a + d/n

None of these

a + (n – 1)d

a + nd

58. 2¹+2²+2³+…+2ⁿ =

2(2ⁿ – 1)

None of these

2(2ⁿ¯¹ – 1)

2(2ⁿ⁺¹ – 1)

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

None of these

-7/5, -5/3, -1,……..

1,2,3, …………..

-2/3, 1, 7/3 ………….

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

Not a sequence

A.P

G.P

A sequence

61. 21 + 22 + 23 + …….. + 2n =

2(2n – 1)

2(2n – 1 – 1)

None of these

2(2n + 1 – 1)

62. The common ratio of a geometric sequence cannot be

63. Geometric sequence cannot contain

None of these

64. 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

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

2ab/a+b

a+b/2

a+b/2ab

ab/a+b

66. No term of an harmonic sequence can be

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

4⁶

None of these

4⁵

4³

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

Common difference

Geometric mean

Common ratio

Arithmetic mean

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

Arithmetic series

Harmonic series

Infinite series

Geometric series

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

2ab/a-b

a-b/2ab

a+b/2ab

2ab/(a+b)

71. 4:32 can be written in

Binomial series

Arithmetic series

Infinite geometric series

None of these

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

-7

-13

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

–4/9

–3/5

5/3

6/5

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

– 2

– 1

75. 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

Page 4 of 4

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

a+b

(a+b)/2

a–b

(a–b)/2

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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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