Harmonic mean

If x, y, z form a harmonic progression, then y is the harmonic mean of x and z. Find the harmonic mean of the numbers 6 and 5.

Correct result:

y =  5.4545

Solution:

x=6 z=5  x1=1/x=1/6=16≐0.1667 x3=1/z=1/5=15=0.2  d=(x3−x1)/2=(0.2−0.1667)/2=160≐0.0167 x2=x1+d=0.1667+0.0167=1160≐0.1833  y=1/x2=1/0.1833=6011=5.4545

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