Harmonic Progression

Harmonic Progression:


Harmonic Progression (HP):

Definition: In mathematics, a harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression.Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.

The general form of the harmonic progression is ,

a , a , a , a .............

1+d 1+2d 1+3d

Example:

10, 10/6 , 10/11 , 10/16....

Here a = 10 and d = 5.


A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progression.
Note:

i) The series formed by the reciprocals of the terms of a geometric series is also a geometric series.
ii) There is no general method of finding the sum of a harmonic progression.
To find the nth term of an H.P

To find the nth term of an H.P, find the nth term of the corresponding A.P. obtained by the reciprocals of the terms of the given H.P. Now the reciprocal of the nth term of an A.P. will be the nth term of the H.P.


There are three types of Progression in math,

*

Arithmetic progression
*

Geometric progression
* Harmonic progression

Hope you like the above example of Harmonic Progression.Please leave your comment if you have any doubts.