Question

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

• A. $ab=cd$
• B. $ac=bd$
• C. $bc=ad$
• D. $noneofthese$

Answer 1

The correct option is C $bc=ad$

$2b=a+c,c=\frac{2bd}{b+d}$
$\Rightarrow 2bd=c(b+d)$
$\Rightarrow (a+c)d=c(b+d)$ [as 2b = a + c]$\Rightarrow ad+cd=bc+cd$
$\Rightarrow bc=ad$