Mathematics Sequences and Series Online Test

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Question 1

1. 2¹+2²+2³+…+2ⁿ =

Answer

2(2ⁿ¯¹ – 1)

Answer

None of these

Answer

2(2ⁿ⁺¹ – 1)

Answer

2(2ⁿ – 1)

Question 2

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

Question 3

3. 2,4,6,8,10,12, ….. is

Answer

Arithmetic series

Answer

Geometric series

Question 4

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

Question 5

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

Answer

r < – 1, r > 1

Answer

– 1 ≤ r ≤ 1

Answer

– 1 < r < 1

Answer

r ≤ – 1, r ≥ 1

Question 6

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

Answer

2 (d – c)

Answer

2 (f – d)

Answer

2 (c – a)

Question 7

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

Answer

Oscillatory

Answer

Convergent

Answer

None of these

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

12. 21 + 22 + 23 + …….. + 2n =

Answer

2(2n + 1 – 1)

Answer

None of these

Answer

2(2n – 1 – 1)

Answer

2(2n – 1)

Question 13

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

Answer

Arithmetic

Answer

None of these

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Answer

None of these

Question 18

18. If n is the total number of arithmetic means between a and b. The formula of mth arithmetic mean between a and b is

Answer

None of these

Answer

a + m(a–b)/n+1

Answer

a + m(b–a)/n+1

Answer

a + n(b–a)/n+1

Question 19

19. If |x| < 1 and y = x-x² + x³-x⁴ + ………….. ∞, then the value of x is

Question 20

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

Answer

y – 1/2y

Question 21

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

Answer

Harmonic series

Answer

Geometric series

Answer

Infinite series

Answer

Arithmetic series

Question 22

22. Nth term of A.P is

Answer

None of these

Answer

a + (n – 1)d

Question 23

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

Answer

n/2 {2a + (n – 1) d}

Answer

a + (n – 1) d

Answer

a (1 – rⁿ)/1 – r

Question 24

24. The two geometric means between a and b are

Answer

a(b/a)¹ᐟ², b

Answer

b(a/b)¹ᐟ², b

Answer

a(b/a)¹ᐟ², b

Question 25

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

Question 26

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

Answer

None of these

Question 27

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

Answer

None of these

Question 28

28. No term of an harmonic sequence can be

Question 29

29. 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

Answer

None of these

Question 30

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

Answer

Harmonic series

Question 31

31. Common fraction of 7.755 is

Question 32

32. Three G.M between 5 & 0.008 are

Answer

1.0,2,0.0.04

Answer

02,0.5.0.6

Answer

None of these

Answer

0.02,0.05,0.06

Question 33

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

Answer

None of these

Question 34

34. 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

Question 35

35. Geometric sequence cannot contain

Answer

None of these

Question 36

36. 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

Answer

None of these

Question 37

37. If n is the total number of geometric mean between a and b than the nth geometric mean between a and b is

Answer

A(b/a)ⁿᐟⁿ⁺¹

Answer

b(b/a)ᵐᐟⁿ⁺¹

Answer

a(b/a)ᵐᐟⁿ⁺¹

Question 38

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

Answer

None of these

Question 39

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

Question 40

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

Answer

Identity function

Answer

Onto function

Question 41

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

Answer

1,3,5,……

Answer

2,3,5,……

Answer

5,3,1,……

Answer

1,3,6,…..

Question 42

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

Answer

Infinite series

Answer

Geometric series

Answer

Arithmetic series

Answer

Harmonic series

Question 43

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

Question 44

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

Answer

Harmonic series

Question 45

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

Question 46

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

Answer

Common ratio

Answer

Arithmetic mean

Answer

Common difference

Answer

Geometric mean

Question 47

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

Question 48

48. 5th term of a G.P. is 2, then the product of first 9 terms is

Answer

None of these

Question 49

49. The common ratio of a geometric sequence cannot be

Question 50

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

Answer

None of these

Question 51

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

Question 52

52. The A.M between 1 – x + x² is

Question 53

53. Which one is true?

Answer

None of these

Question 54

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

Answer

Arithmetic series

Answer

Harmonic series

Answer

Geometric series

Answer

Infinite series

Question 55

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

Question 56

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

Question 57

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

Question 58

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

Answer

A sequence

Answer

Not a sequence

Question 59

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

Question 60

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

Answer

A sequence

Answer

Not a sequence

Question 61

61. 4:32 can be written in

Answer

None of these

Answer

Arithmetic series

Answer

Infinite geometric series

Answer

Binomial series

Question 62

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

Question 63

63. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

Question 64

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

Answer 86

None of these

Answer 87

1,2,3, …………..

Answer 88

-2/3, 1, 7/3 ………….

Answer 89

-7/5, -5/3, -1,……..

Answer 90

None of these

Answer 91

17, 4n – 3

Answer 92

17, 3n – 4

Answer 93

4n – 3, 17

Answer 94

Infinite series

Answer 95

Arithmetic series

Answer 96

Harmonic series

Answer 97

Geometric series

Answer 98

arⁿ⁺¹

Answer 99

Not a sequence

Answer 100

A sequence

Answer 101

Real numbers

Total Questions:	76
Time Allowed:	40 Minutes
Total Marks:	76
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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