Question

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

• A. not in AP/GP/HP
• B. in AP
• C. in GP
• D. in HP

Answer 1

Answer: (D)

in HP

Given $a,b,c,d$ are in AP

$\Rightarrow \frac{1}{a},\frac{1}{b},\frac{1}{c},\frac{1}{d}$ are in HP

$\Rightarrow \frac{1}{d},\frac{1}{c},\frac{1}{b},\frac{1}{a}$ are in HP

$\Rightarrow \frac{abcd}{d},\frac{abcd}{c},\frac{abcd}{b},\frac{abcd}{a}$ are in HP

$\Rightarrow abc,abd,acd,bcd$ are in HP