Question

If the mth, nth and pth terms of an AP and GP be equal and be respectively x, y, z, then

• A.
• B.
• C.
• D. None of the these

Answer 1

The correct option is A

$A+(m-1)d=xA+(n-1)d=yA+(p-1)d=z\Rightarrow \frac{x-y}{m-n}=\frac{y-z}{n-p}AndA{R}^{m-1}=xA{R}^{n-1}=yA{R}^{p-1}=y\Rightarrow R^{m-1}=\frac{x}{y}and{R}^{n-p}=\frac{x}{z}$
From Eqs.(i)and(ii),we get
${\left[\frac{x}{y}\right]}^{y-z}={\left[\frac{y}{z}\right]}^{x-y}$