# 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. For Harmonic Progression Formulas

For How to Solve Quickly of Harmonic Progression Problems

For Tips and Tricks and Shortcuts of Harmonic Progression

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. $\frac{513}{3233}$

$\frac{513}{3233}$

$\frac{11}{35}$

$\frac{11}{35}$

$\frac{81}{63}$

$\frac{81}{63}$

$\frac{897}{41}$

$\frac{897}{41}$