Thank you for reporting, we will resolve it shortly
Q.
If a, b, c are three consecutive terms of an AP and x, y, z are three consecutive terms of a GP, then the value of $x^{b -c} . y^{c-a} . z^{a-b}$ is
Given $a , b , c$ are in $A \cdot P$
$ \Rightarrow \,b - c =- d , c - a =2 d , a - b =- d$
And $x , y , z$ are in $G.P$
$ \Rightarrow \,y ^{2}= xz$
Now $ x^{b-c} \cdot y^{c-a} \cdot z^{a-b} =x^{-d} \cdot y^{2 d} \cdot z^{-d}$
$=x^{-d} \cdot(x z)^{d} \cdot z^{-d}=1 $