# Harmonic Progressions Questions and Answers

## Harmonic Progression Questions and Answers in Aptitude

A Harmonic progression is a kind of sequence of real numbers made after procuring the reciprocal of the arithmetic progression. Consistently, it is also a classification of real numbers in a way that any term in the order is the harmonic mean of its two fellow numbers. Harmonic Progression Questions and Answers is very important to Know . Furthermore, if the converse of a sequence follows the rule of an arithmetic progression, then it is known as the harmonic progression. It basically means that if a, a+d, a+2d, and so on is an A.P. then $\frac{1}{a}, \frac{1}{(a+d)}, \frac{1}{(a+2d)}$, and so on is known as H.P.

There are Many Applications of Harmonic Progression. In this Page Harmonic progression Questions is given for your Practices.  Question 1 Time: 00:00:00
Find the 6th and 9th term of the series 6, 4, 3, … $\frac{12}{5}, \frac{4}{3}$

$\frac{12}{5}, \frac{4}{3}$

$\frac{8}{5},\frac{7}{11}$

$\frac{8}{5},\frac{7}{11}$

$\frac{4}{3},\frac{12}{7}$

$\frac{4}{3},\frac{12}{7}$

$\frac{12}{7},\frac{6}{5}$

$\frac{12}{7},\frac{6}{5}$

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Question 2 Time: 00:00:00
Find the harmonic mean of 2, 4, and 6 0.45

0.45

1.34

1.34

4.12

4.12

3.27

3.27

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Question 3 Time: 00:00:00
Given the following frequency distribution of second year students of a particular college, calculate the harmonic mean.

 Age (Years) 15 16 17 18 19 Number Of Students 3 7 13 2 5 18

18

19

19

17

17

16

16

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Question 4 Time: 00:00:00
Calculate the harmonic mean for the data given below:

 Marks 30-39 40-49 50-59 60-69 70-79 80-89 90-99 F 7 25 32 20 11 3 2 54

54

64

64

74

74

44

44

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Question 5 Time: 00:00:00
If x, y, z are in h.p, then y is connected with x and z as : $2\times\frac{1}{y} = \frac{1}{x} + \frac{1}{z}$

$2\times\frac{1}{y} = \frac{1}{x} + \frac{1}{z}$

$2 \times\frac{1}{z} = \frac{1}{y} + \frac{1}{z}$

$2 \times\frac{1}{z} = \frac{1}{y} + \frac{1}{z}$

$2 \times\frac{1}{x} = \frac{1}{x} + \frac{1}{y}$

$2 \times\frac{1}{x} = \frac{1}{x} + \frac{1}{y}$

None of the mentioned

None of the mentioned

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Question 6 Time: 00:00:00
For 2 number X.Y, Harmonic Mean among them will be? $\frac{2y +2x}{3y}$

$\frac{2y +2x}{3y}$

$\frac{2xy}{x+y}$

$\frac{2xy}{x+y}$

$\frac{(x+y)}{2xy}$

$\frac{(x+y)}{2xy}$

$\frac{2y}{(x+y)}$

$\frac{2y}{(x+y)}$

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Question 7 Time: 00:00:00
From the given data 5, 10,17,24,30 calculate H.M. 12.123

12.123

11.526

11.526

10.324

10.324

11.932

11.932

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Question 8 Time: 00:00:00
If the sum of reciprocals of first 9 terms of an HP series is 81, find the 5th term of HP. 10

10

9

9

$\frac{1}{9}$

$\frac{1}{9}$

$\frac{1}{8}$

$\frac{1}{8}$

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Question 9 Time: 00:00:00
The 3rd term of an HP is 5 and the 6th term is 8. Find the maximum possible number of terms in H.P. 12

12

9

9

10

10

13

13

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Question 10 Time: 00:00:00
Find maximum partial sum of harmonic progression, if second and third terms are $\frac{1}{13}$ and $\frac{1}{10}$ respectively. 1.23

1.23

1.63

1.63

1.25

1.25

1.09

1.09

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Question 11 Time: 00:00:00
The sixth term of H.P. is $\frac{9}{106}$ and seventh term is $\frac{9}{122}$. Find the sum of its second and fifth term. $\frac{513}{3233}$

$\frac{513}{3233}$

$\frac{11}{35}$

$\frac{11}{35}$

$\frac{81}{63}$

$\frac{81}{63}$

$\frac{897}{41}$

$\frac{897}{41}$

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Question 12 Time: 00:00:00
x , y ,z are said to be in harmonic progression if the reciprocals $\frac{1}{x},\frac{1}{y},\frac{1}{z}$ are in a.p. find out the value of A for which 13,a,16 are in harmonic progression 12.23

12.23

13.66

13.66

14.34

14.34

15.78

15.78