Short tutorial on how to calculate harmonic progression from arithmetic progression with formula and example.
Harmonic Progression in mathematical geometry is a sequence of real
numbers formed by taking the reciprocals of an arithmetic progression.
Example: The sequence 1,2,3,4,5 is an arithmetic progression, so its reciprocals 1/1,1/2,1/3,1/4,1/5 are harmonic progression.
Harmonic Progression Series and Formula:
Harmonic Progression (H.P) = 1/a , 1/a+d, 1/a+2d, 1/a+3d.........1/a+kd
a is the starting number in the sequence
d is the common difference between the numbers given in the sequence.
Let us learn here how to calculate harmonic progression from arithmetic progression with a neat example.
Example: Consider the sequence of arithmetic progression 3,5,7,9,11. Calculate harmonic progression.
A.P = 3,5,7,9,11
Starting Sequence = 3
Common Difference = 2
Applying the values in the formula,
Harmonic Progression (H.P) = 1/3 , 1/3+2, 1/3+2(2), 1/3+3(2), 1/3+4(2)
Harmonic Progression (H.P) = 1/3 , 1/5, 1/7, 1/9, 1/11