Question

three numbers are in harmonic progression. their mean is 20.if the first term is twice the third term find the three numbers???

Answer 1

let the three numbers be
1/a, 1/(a+d), 1/(a+2d)

1/a = 2/(a+d)
2a = a+d
a = d

so the three numbers are
1/a , 1/(2a), 1/(3a)

(1/a + 1/(2a) + 1/(3a) )/3 = 20
LCD = 6a
6/6a + 3/6a + 2/6a = 60
11/6a = 60
360a = 11
a = 11/360 , d = 11/360

the three numbers are:
360/11, 360/22, 360/33
or, in reduced form

360/11, 180/11, 120/11