  Question:

What is the harmonic progression between a,b,c,d

Posted by: Sai on 31.05.2020  Prabhat R. from Kolkata
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answer is 1/a, 1/b, 1/c, 1/d provided given numbers (a, b, c, d) are in A.P..

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Avinash R. from Patna
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Harmonic progression is determined by taking the reciprocals of the arithmetic progression that does not contain 0. For example, the sequence a, b, c, d, …is considered as an arithmetic progression, the harmonic progression can be calculated as 1/a, 1/b, 1/c, 1/d.

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Laxmi S. from Burdwan
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1/a,1/b,1/c,1/d are Harmonic progression. • Like

Answer:  a,b,c,d will be in Harmonic Progression provided their reciprocals 1/a,1/b,1/c and 1/d are in Arithmetic

Progression.     That is( 1/a-1/b) = (1/b-1/c)  =(1/c-1/d).

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Priya V. from Delhi
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Before answering this question, I would like to tell about the Harmonic Progression. The terms a, b, c are said to be in harmonic progression if 1/a, 1/b, and 1/c are in Arithmetic Progression, and we know that the difference of two consecutive terms of AP are constant and called as common difference. Here the four terms are given as a, b, c, and d. So 1/a, 1/b, 1/c, and 1/d would be AP and the difference between these consective terms would be same.

We can have the following relation with the above concept.

1/b - 1/a = 1/c - 1/b = 1/d - 1/c

or (a-b)/ab = (b-c)/bc = (c-d)/cd

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Satheesh O. from Kochi
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A Harmonic Progression (HP) is defined as a sequence of real numbers which is determined by taking the reciprocals of the arithmetic progression that does not contain 0.  The sequence a, b, c, d, …is considered as an arithmetic progression, the harmonic progression can be calculated as 1/a, 1/b, 1/c, 1/d, …

• Answered by: Anonymous from Bhubaneswar
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1/a,1/b,1/c, 1/d is the HP between a, b,c ,d

If a, b, c, d in HP then, 1/b-1/a =1/d-1/c

cd(a-b)=ab(c-d)

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Satyam K. from Gurgaon
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If u feel good solution then like V
Vaibhav P. from Kanpur
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1/a,1/b,1/c,1/d Lohitha G. from Kharagpur
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Harmonic progression of a,b,c,d will be 1/a,1/b,1/c,1/d provided a,b,c,d ae in arithmetic progression
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Kapil S. from Agra
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1/a,1/b,1/c,1/d
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Malika from Bangalore
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1/a,1/b,1/c,1/d

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