Let the number be a/2, a, ar. which are in G.P.
i.e., a/2 + a + ar = 30/10
and a/r.a, a r = 1
⇒ a3 = 1
∴ a = 1
put a = 1 in (1)
1/r + 1 + r = 30/10
⇒ (1 + r + r2)/r = 39/10
⇒ 10 + 10r + 10r3 = 39
r ⇒ 10r2 - 29r + 10 = 0
⇒ r = 5/2 and 2/5
∴ The menson are : a/r, a, ar
⇒ (1/5)/2, 1, (1 - 5)/2 = 2/5, 1, 5/2
⇒ 5/2, 1, 2/5
