A number of terms are said to be in Harmonic Progression (H.P) if their reciprocals are in A.P.
, the term of the H.P, is given by , where and
Harmonic Mean (H.M)
If are in H.P, then their Harmonic Mean (H.M) is given by
This means reciprocals of the Harmonic mean is the Arithmetic Mean of the reciprocals.
Some Facts about H.P -:
(i) If and are two non-zero numbers, then the harmonic mean of and is number.
such that the sequence is a H.P.
We have or
(ii) If are non-zero numbers, then the harmonic mean of these numbers is given by
(iii) The numbers are said to be harmonic means between and , if are in H.P, i.e. if are in A.P.
Let be the common difference of this AP.