Question

Let the positive numbers $a,b,c,d$ be in A.P. Then $abc,abd,acd,bcd$ are

• A. Not in A.P./G.P./H.P.
• B. In A.P.
• C. In G.P.
• D. In H.P.

Answer 1

The correct option is D In H.P.

Since $a,b,c,d$ are in A.P.
then $\frac{1}{a},\frac{1}{b},\frac{1}{c},\frac{1}{d}$ are in H.P.
Also $\frac{1}{d},\frac{1}{c},\frac{1}{b},\frac{1}{a}$ are also in H.P.
Multiply $abcd$ in above expression
$abcd\times \frac{1}{d},abcd\times \frac{1}{c},abcd\times \frac{1}{b},abcd\times \frac{1}{a}$
Hence $abc,abd,acd,bcd$ are in H.P.