Harmonic Progression (H.P.)
Definition
The sequence a1,
a2, a3.......an......(ai > 0) is said to be an H.P. if the
sequence 
is an A.P.
Term of H.
P. :.
The
nth term, an, of the H.P. is 
Note: There
is no formula for the sum of n terms of an H.P.
Harmonic Means:
- If a and b are two non-zero numbers, then the harmonic
mean of a and b is a number H such that the numbers a, H, b are in H.P. We have.
- If a1, a2, .......an
are ‘n’ non-zero numbers, then the harmonic mean H of these numbers is given
by
. - The n numbers H1,
H2,.......,Hn are said to be n-harmonic means between a
and b, if a , H1 , H2 ........, Hn
, b are in H.P. i.e if
are in A.P.. Let d
be the common difference of the A.P., then 
&⇒ d = 
- Thus
.
Example 1
Find the 4th and the 8th terms of the
H.P. 6, 4, 3,……….
Solution:
Consider 
Here T2 – T1 = T3 – T2
= 
&⇒
,….. is an A.P.
4th term of this A.P. = 
+ 3 ´ = + 
= 
,
and the 8th term = + 7 ´ = 
Hence the 4th term
of the H.P. = 
and the 8th term =
