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. 3ac
• D. None of these

Answer 1

The correct option is A

3ad

Since a, b, c, d are in H.P., therefore b is the H.M. of a and c

i.e., b = $\frac{2ac}{b+d}$, $\therefore (a+c)(b+d)$ = $\frac{2ac}{b}.\frac{2bd}{c}$

$\Rightarrow ab+ad+bc+cd$ = 4ad $\Rightarrow ab+bc+cd$ = 3ad

Trick : Check for a =1, b = $\frac{1}{2}$, c = $\frac{1}{3}$, d = $\frac{1}{4}$