Question

If $a,b,c,d$ are in $H.P$ , then $ab+bc+cd$ is equal to

• A. $3ad$
• B. $(a+b)(c+d)$
• C. $ac$
• D. $Noneofthese$

Answer 1

The correct option is A $3ad$

Since $a,b,c$ are in H.P, so $b=\frac{2ac}{a+c}$.

Also, $b,c,d$ are in H.P, so $c=\frac{2bd}{b+d}$.

Therefore, $(a+c)(b+d)=\frac{2ac}{b}\times \frac{2bd}{c}$

$\Rightarrow ab+cb+ad+cd=4ad$

$\Rightarrow ab+bc+cd=3ad$

Hence, option 'A' is correct.