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: ?->(Show Answer!)

1. 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:

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By: anil on 05 May 2019 02.39 am

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

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MCQ->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:....