If p, q and r are three unequal numbers such that p, q and r are in AP
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
- 1 : 2 : 3
- 2 : 3 : 4
- 3 : 2 : 1
- 1 : 3 : 4
Solution
p, q and r are in A.P.
q - p = r - q
2q = p + r
By plugging in values, option D cannot be correct.
p, r-q and q-p are in G.P.
(r-q)2 = p(q-p)
r-q = p as r-p = q-p
r = p+q
By plugging in values, only A and D satisfies this relation.
The correct option is A.