Question

56. (c) We have, ( frac{a-x}{p x}=frac{a-y}{q y}=frac{a-z}{r z}=lambda(text { say }) )
( Rightarrow p=frac{a-x}{lambda x}, q=frac{a-y}{lambda y}, r=frac{a-z}{lambda z} )
Now ( p, q, r ) are in A.P.
( Rightarrow quad frac{a-x}{lambda x}, frac{a-y}{lambda y}, frac{a-z}{lambda z} ) are in A.P.
( Rightarrow quad frac{a-x}{x}, frac{a-y}{y}, frac{a-z}{z} ) are in A.P.
( Rightarrow quad frac{a}{x}-1, frac{a}{y}-1, frac{a}{z}-1 ) are in A.P.
( Rightarrow quad frac{a}{x}, frac{a}{y}, frac{a}{z} ) are in A.P.
( Rightarrow quad frac{1}{x}, frac{1}{y}, frac{1}{z} ) are in ( mathrm{A} . P )
( Rightarrow x, y, z ) are in HP.

# a-x a -y _ 0-2 and p, q, r be in A.P., then., Y. qy rz 56. If a - px z are in (a) A.P. (b) G.P. (c) H.P. (d) None of these

Solution