Mathematics Sequences and Series Online Test

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You can prepare for Mathematics Sequences and Series Online Test by attempting the free online quizzes at Gotest.com.pk. We provide instant results, performance reports, and detailed explanations for every question.

Question 1

1. 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

a + m(b–a)/n+1

Answer

a + n(b–a)/n+1

Answer

None of these

Answer

a + m(a–b)/n+1

Question 2

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

Question 3

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

Answer

arⁿ⁺¹

Question 4

4. 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 5

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

Question 6

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

Question 7

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

Answer

17, 4n – 3

Answer

17, 3n – 4

Answer

4n – 3, 17

Question 8

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

Question 9

9. 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 10

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

Question 11

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

Answer

Arithmetic series

Answer

Infinite series

Answer

Geometric series

Answer

Harmonic series

Question 12

12. The A.M between 1 – x + x² is

Question 13

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

Question 14

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

Answer

None of these

Question 15

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

Answer

None of these

Question 16

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

Answer

None of these

Question 17

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

Answer

n/2 {2a + (n – 1) d}

Answer

a (1 – rⁿ)/1 – r

Answer

a + (n – 1) d

Question 18

18. 2,4,6,8,10,12, ….. is

Answer

Arithmetic series

Answer

Geometric series

Question 19

19. 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 20

20. Nth term of A.P is

Answer

a + (n – 1)d

Answer

None of these

Question 21

21. 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 22

22. No term of an harmonic sequence can be

Question 23

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

Question 24

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

Question 25

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

Question 26

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

Answer

None of these

Question 27

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

Answer

Infinite series

Answer

Harmonic series

Answer

Arithmetic series

Answer

Geometric series

Question 28

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

Question 29

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

Question 30

30. 2¹+2²+2³+…+2ⁿ =

Answer

2(2ⁿ – 1)

Answer

None of these

Answer

2(2ⁿ⁺¹ – 1)

Answer

2(2ⁿ¯¹ – 1)

Question 31

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

Question 32

32. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

Question 33

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Answer

y – 1/2y

Question 39

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

Answer

Not a sequence

Answer

A sequence

Question 40

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

Answer

Harmonic series

Answer

Infinite series

Answer

Arithmetic series

Answer

Geometric series

Question 41

41. 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 42

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

Question 43

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

Question 44

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

Answer

None of these

Question 45

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

Answer

Arithmetic

Answer

None of these

Question 46

46. 21 + 22 + 23 + …….. + 2n =

Answer

2(2n – 1)

Answer

None of these

Answer

2(2n – 1 – 1)

Answer

2(2n + 1 – 1)

Question 47

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

Answer

Arithmetic series

Answer

Geometric series

Answer

Infinite series

Answer

Harmonic series

Question 48

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

Answer

None of these

Question 49

49. 5th term of a G.P. is 2, then the product of first 9 terms is

Answer

None of these

Question 50

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

Question 51

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

Question 52

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

Answer

None of these

Answer

Convergent

Answer

Oscillatory

Question 53

53. 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 54

54. 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 55

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

Question 56

56. Common fraction of 7.755 is

Question 57

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

Answer

Not a sequence

Answer

A sequence

Question 58

58. 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 59

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

Question 60

60. The common ratio of a geometric sequence cannot be

Question 61

61. Three G.M between 5 & 0.008 are

Answer

0.02,0.05,0.06

Answer

None of these

Answer

02,0.5.0.6

Answer

1.0,2,0.0.04

Question 62

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

Answer

– 1 ≤ r ≤ 1

Answer

r < – 1, r > 1

Answer

– 1 < r < 1

Answer

r ≤ – 1, r ≥ 1

Question 63

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

Question 64

64. Geometric sequence cannot contain

Answer

None of these

Answer 77

Harmonic series

Answer 78

Common ratio

Answer 79

Geometric mean

Answer 80

Arithmetic mean

Answer 81

Common difference

Answer 82

-2/3, 1, 7/3 ………….

Answer 83

-7/5, -5/3, -1,……..

Answer 84

None of these

Answer 85

1,2,3, …………..

Answer 86

Arithmetic series

Answer 87

Infinite geometric series

Answer 88

Binomial series

Answer 89

None of these

Answer 90

Real numbers

Answer 91

2 (d – c)

Answer 92

2 (c – a)

Answer 93

2 (f – d)

Answer 94

Identity function

Answer 95

Onto function

Answer 96

None of these

Answer 97

None of these

Answer 98

1,3,5,……

Answer 99

2,3,5,……

Answer 100

1,3,6,…..

Answer 101

5,3,1,……

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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