Progressions

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. 1 : 2 : 3
  2. 2 : 3 : 4
  3. 3 : 2 : 1
  4. 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.