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

Question 2

2. 2,4,6,8,10,12, ….. is

Answer

Arithmetic series

Answer

Geometric series

Question 3

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

Question 4

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

Answer

17, 4n – 3

Answer

4n – 3, 17

Answer

17, 3n – 4

Question 5

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

Question 6

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

Question 7

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

Question 8

8. Geometric sequence cannot contain

Answer

None of these

Question 9

9. No term of an harmonic sequence can be

Question 10

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

Answer

1,2,3, …………..

Answer

-2/3, 1, 7/3 ………….

Answer

-7/5, -5/3, -1,……..

Answer

None of these

Question 11

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

Question 12

12. 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

r ≤ – 1, r ≥ 1

Answer

– 1 < r < 1

Question 13

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

Answer

y – 1/2y

Question 14

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

Answer

None of these

Question 15

15. Three G.M between 5 & 0.008 are

Answer

None of these

Answer

02,0.5.0.6

Answer

1.0,2,0.0.04

Answer

0.02,0.05,0.06

Question 16

16. 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 17

17. 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 18

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

Answer

None of these

Question 19

19. Which one is true?

Answer

None of these

Question 20

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

Question 21

21. 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)ᵐᐟⁿ⁺¹

Answer

b(b/a)ᵐᐟⁿ⁺¹

Answer

A(b/a)ⁿᐟⁿ⁺¹

Question 22

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

Question 23

23. 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 24

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

Question 25

25. 4:32 can be written in

Answer

Binomial series

Answer

Infinite geometric series

Answer

Arithmetic series

Answer

None of these

Question 26

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

Question 27

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

Answer

None of these

Question 28

28. Common fraction of 7.755 is

Question 29

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

Answer

Geometric series

Answer

Harmonic series

Answer

Arithmetic series

Answer

Infinite series

Question 30

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

Question 31

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

Answer

A sequence

Answer

Not a sequence

Question 32

32. Nth term of A.P is

Answer

None of these

Answer

a + (n – 1)d

Question 33

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

Question 34

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

Question 35

35. 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 36

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

Question 37

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

Answer

Harmonic series

Question 38

38. 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 39

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

Answer

Real numbers

Question 40

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

Answer

Harmonic series

Answer

Arithmetic series

Answer

Geometric series

Answer

Infinite series

Question 41

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

Question 42

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

Question 43

43. 2¹+2²+2³+…+2ⁿ =

Answer

None of these

Answer

2(2ⁿ⁺¹ – 1)

Answer

2(2ⁿ – 1)

Answer

2(2ⁿ¯¹ – 1)

Question 44

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

Answer

Convergent

Answer

Oscillatory

Answer

None of these

Question 45

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

Answer

None of these

Question 46

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

Answer

None of these

Answer

Arithmetic

Question 47

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

Answer

Geometric series

Answer

Infinite series

Answer

Arithmetic series

Answer

Harmonic series

Question 48

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

Question 49

49. The common ratio of a geometric sequence cannot be

Question 50

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

Answer

a (1 – rⁿ)/1 – r

Answer

n/2 {2a + (n – 1) d}

Answer

a + (n – 1) d

Question 51

51. 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 52

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

Question 53

53. 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 54

54. 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 55

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

Answer

2 (f – d)

Answer

2 (d – c)

Answer

2 (c – a)

Question 56

56. 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 57

57. 9th term of the sequence 25/3, 1/3, 1/6 --------- is

Question 58

58. 21 + 22 + 23 + …….. + 2n =

Answer

None of these

Answer

2(2n – 1 – 1)

Answer

2(2n + 1 – 1)

Answer

2(2n – 1)

Question 59

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

Question 60

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

Question 61

61. 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 62

62. 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 63

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

Answer

Arithmetic mean

Answer

Geometric mean

Answer

Common ratio

Answer

Common difference

Question 64

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

Answer 89

Identity function

Answer 90

Onto function

Answer 91

Geometric series

Answer 92

Infinite series

Answer 93

Harmonic series

Answer 94

Arithmetic series

Answer 95

None of these

Answer 96

None of these

Answer 97

a + n(b–a)/n+1

Answer 98

a + m(b–a)/n+1

Answer 99

a + m(a–b)/n+1

Answer 100

None of these

Answer 101

None of these

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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