If p, q and r are three unequal numbers such that p, q and r are in A.P., and p, r-q and q-p are in G.P., then p : q : r is equal to:

Given that p, q and r are in A.P., 

2q = p + r

p = 2q - r                                   Eq -1

Given that p, r-q and q-p are in G.P.,

Let us assume the common ratio of k in G.P.

r-q = k(p)                                   Eq -2

q-p = k(r-q)                               Eq -3

q-p = $$k^{2}$$(p)                               Eq -4

Substitute Eq-1 in Eq-3,

q-(2q-r) = k(r-q)

r-q = k(r-q)

So, k=1

From Eq -4, we get q=2p

Now substitute q=2p in Eq-1 we get r=3p

Hence, ratio of p:q:r = p:2p:3p = 1:2:3