Question

can anyone tell me the formula of Harmonic progression

Answer 1

Hi

Here is your answer,

A progression whose reciprocals are in A.P is called Harmonic Progression.

    If the sequence FORMULA:- 1/a₁, 1/a₂ , 1/a₃ ,............., 1/an is an A.P

nth Term of Harmonic Progression

(a) nth term of the H.P from the beginning 

                            an = 1/1/a₁ + (n - 1 ) ( 1/a₂ - 1/a₁) 

                             =   a₁ × a₂/a₂ + (n -1 ) ( a₁ - a₂)

(b) nth term of the HP from the end 

a'n = 1/ 1/an - ( n - 1) ( 1/a₂ - 1/a₁) = a₁ a₂ a₃/ a₁ a₂ - an (n-1) ( a₁ - a₂)

 c) 1/an + 1/a'n = 1/a + 1/an

                         = 1/first term of AP + 1/ last term of AP

d) an = 1/a + (n-1)d , if a,d are the first term and common difference of the corresponding AP.


HOPE IT HELPS YOU !