Question

If $a,b,c$ are in GP. and $a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}},$ then $x,y,z$ are in

• A. A.P
• B. G.P
• C. H.P
• D. None

Answer 1

The correct option is A A.P

Let $a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}}=k$
$b^2=ac$
$a=k^x,b=k^y,c=k^z$
$k^{2}y=k^x\times k^z$
$2y=x+z$
$y+y=x+z$
$y-x=z-y$
Hence $x,y,z$ are in A.P.