Harmonic Progressions

What is a Harmonic Progression?

Harmonic Progressions are sequences of numbers obtained by taking the reciprocals of numbers in Arithmetic Progression. To learn more about Arithmetic Progressions, you can read this blog post here.

Consider an arithmetic progression as follows:
1, 4, 7, 10, ...
If we take the reciprocals of each term in the above arithmetic progression, we obtain the following sequence of numbers:
1, 1/4, 1/7, 1/10, ...
The above progression is an example of a harmonic progression.

General form or standard form of a Harmonic Progression

An arithmetic progression can be represented as follows:
a, a + d, a + 2d, a + 3d, ...
Correspondingly, a harmonic progression can be represented as follows:
1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d), ...
General term of harmonic progression
Tn = 1/(a + (n - 1)d)
where a is the first term of the corresponding arithmetic progression and d is its common difference.

To prove that three numbers are in harmonic progression

If three numbers a, b and c are in Harmonic Progression, then
b = 2ac/(a + c)

1 comment:

  1. I am here to discuss more about harmonic progression.A harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression. In other words, it is a sequence of the form.