HARMONIC PROGRESSION (HP) - Concept and Properties with Example

HARMONIC PROGRESSION (H.P.)

A sequence is said to be in H.P. if the reciprocal of its terms are in AP.

If the sequence a1, a2, a3, ......., an is an HP then 1/a1, 1/a2,........., 1/an is an AP . Here we do not have the formula for the sum of the n terms of an HP.

The general form of a harmonic progression is

Properties :

  1. No term of any H.P. can be zero.
  2. If a, b, c are in HP, then

     

     

    Example :

    The sum of three numbers are in H.P. is 37 and the sum of their reciprocals is 4 . Find the numbers.

     

    Solution :

     

     

    Example :

     Suppose a is a fixed real number such that a-x/px =a-y/qy = a-z/rz

    If p, q, r are in A.P., then prove that x, y, z are in H.P.

     

    Solution :

Post By : Preeti Rai 20 Apr, 2019 3571 views Maths