In a harmonic sequence, the first term is 1/2, and the third term is 1/8. The harmonic mean between the two terms is

Answer 1

1/5= 2nd term

Harmonic mean = 2xy/(x+y) with x=1/2= 1st term, y=1/8=3rd term

replace x by 1/2 and y by 1/8

plug them into the formula for Harmonic mean

H= 2(1/2)(1/8)/(1/2 + 1/8)

= (1/8)/(5/8)= 1/5

another method:

the Harmonic mean = the average of the reciprocals of 1/2 and 1/8:

1/H = (1/x + 1/y)/2 = [1/(1/2)+ 1/(1/8)]/2 = (2+8)/2 = 10/2 = 5

1/H=5

H= 1/5

another method is (8-2)/2 = 6/2 = 3

the denominator increases by 3 for each term

1/x, 1/(x+3), 1/(x+6), 1/(x+9), ...

where 1/x is the 1st term = 1/2

1/2, 1/(2+3), 1/(2+6), 1/(2+9), ...

1/2, 1/5, 1/8, 1/11, ...

The Harmonic mean is one of several Greek means, originally named by Aristotle as the Pythagorean mean. It's related to the perfect 4th interval in music theory. It's also used in finance calculations.