Let the three numbers be a/r, a, ar
So, according to the question
a/r × a × ar = 125 … equation (1)
From equation (1) we get,
a3 = 125
a = 5
a/r × a + a × ar + ar × a/r = 87 1/2
a/r × a + a × ar + ar × a/r = 195/2
a2/r + a2r + a2 = 195/2
a2 (1/r + r + 1) = 195/2
Substituting a = 5 in above equation we get,
52 [(1 + r2 + r)/r] = 195/2
1 + r2 + r = (195r/2 × 25)
2(1 + r2 + r) = 39r/5
10 + 10r2 + 10r = 39r
10r2 – 29r + 10 = 0
10r2 – 25r – 4r + 10 = 0
5r(2r - 5) – 2(2r -5) = 0
r = 5/2, 2/5
So G.P is 10, 5, 5/2 or 5/2, 5, 10
∴ The three numbers are 10, 5, 5/2 or 5/2, 5, 10