Question:

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

Posted by: Sai on 31.05.2020

answer is 1/a, 1/b, 1/c, 1/d provided given numbers (a, b, c, d) are in A.P..

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.

1/a,1/b,1/c,1/d are Harmonic progression.

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).

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

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, …

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)

If u feel good solution then like
1/a,1/b,1/c,1/d
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
1/a,1/b,1/c,1/d
1/a,1/b,1/c,1/d

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