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.
- Standard form of an H.P is
The terms are reciprocals of an A.P.
- H.M between is
- A > G > H.
Note: Any sum in H.P can be solved by converting it into an A.P.
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 =
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
From (1), we get
Substitute in (3)