Posted on - 09-02-2017

IIT JEE

The sequence a_{1},
a_{2}, a_{3}.......a_{n}......(a_{i} > 0) is said to be an H.P. if the
sequence is an A.P.

Term of H. P. :.

The
nth term, a_{n}, of the H.P. is

Note: There is no formula for the sum of n terms of an H.P.

- 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 a
_{1}, a_{2}, .......a_{n}are ‘n’ non-zero numbers, then the harmonic mean H of these numbers is given by . - The n numbers H
_{1}, H_{2},.......,H_{n}are said to be n-harmonic means between a and b, if a_{ }, H_{1}, H_{2}........, H_{n}, 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 .

Find the 4th and the 8th terms of the H.P. 6, 4, 3,……….

Consider

Here T_{2} – T_{1} = T_{3} – T_{2}
=

&⇒
,….. 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 =