Mathematics - Sequence & Series Question with Solution | TestHub

$x=1+a+a^2=......$

$x=\frac{1}{1-a}\Rightarrow a=1-\frac{1}{x}$

$y=\frac{1}{1-b}\Rightarrow b=1-\frac{1}{y}$

$z=\frac{1}{1-c}\Rightarrow c=1-\frac{1}{z}$

$a,b,c$ are in A.P.

$\Rightarrow 1-\frac{1}{x},1-\frac{1}{y},1-\frac{1}{z}$ are in A.P.

$\Rightarrow -\frac{1}{x},-\frac{1}{y},-\frac{1}{z}$ are in A.P.

$\Rightarrow \frac{1}{x},\frac{1}{y},\frac{1}{z}$ are in A.P.