Question

a, b, c, d $\in R^{+}$ such that a, b, and c are in A.P. and b,c and, d are in H.P., then

• A. ab =cd
• B. ac =bd
• C. bc =ad
• D. none of these

Answer 1

The correct option is C

bc =ad

$2b=a+c,c=\frac{2bd}{b+d}$

$\Rightarrow 2bd=c(b-d)$

$\Rightarrow (a+c)d=c(b+d)[as2b=a+c]$

$\Rightarrow ad+cd=bc=cd$

$\Rightarrow bc=ad$