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 $d,c,b,a$ are in A.P

$\Rightarrow \frac{1}{d},\frac{1}{c},\frac{1}{b},\frac{1}{a}$ are in H.P

$\Rightarrow \frac{abcd}{d},\frac{abcd}{c},\frac{abcd}{b},\frac{abcd}{a}$ are in H.P

$\Rightarrow abc,abd,acd,bcd$ are in H.P