Question

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

• A. $0$
• B. $xyz$
• C. $-1$
• D. $1$

Answer 1

The correct option is D $1$

Let $d$ be the common difference of the AP
and $r$ be the common ratio of GP.
Then $b=a+d,c=a+2d$
and $y=xr,z=x{r}^2$

Now, $x^{b-c}.y^{c-a}.z^{a-b}$
$=x^{-d}.(xr{)}^{2d}.(x{r}^2{)}^{-d}$
$=\left(x^{-d+2d-d}\right)\times (r{)}^{2d-2d}$
$=x^0\times y^0=1$