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Introduction to Harmonic Progression

Note: This is not mentioned in the syllabus; but is important for competitive examinations. Some details are provided here, so that questions based on H.P can be attempted.

  1. Standard form of an H.P is

    The terms are reciprocals of an A.P.
  2. The
  3. H.M between is
  4. A > G > H.

Note: Any sum in H.P can be solved by converting it into an A.P.


Example 1:
The first and second terms of a H.P are respectively, find the term.

If are terms of a H.P
3 and 5 are terms of an A.P.
term of the A.P =


Example 2:
If the A.M between two numbers is 1, prove that their H.M is the square of their G.M.

Let the two numbers be
A.M =
G.M =
H.M =
From (1), we get
Substitute in (3)


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