Question
If the positive integers $$a, b, c, d$$ are in A.P., then the numbers $$abc, abd, acd, bcd$$ are in
A.
H.P.
B.
A.P.
C.
G.P.
D.
None of the above
Answer :
H.P.
Solution :
Given, $$a, b, c, d$$ are in A.P.
$$\eqalign{
& \Rightarrow \frac{1}{a},\frac{1}{b},\frac{1}{c},\frac{1}{d}{\text{are in H}}{\text{.P}}{\text{.}} \cr
& \Rightarrow \frac{1}{d},\frac{1}{c},\frac{1}{b},\frac{1}{a}{\text{are also in H}}{\text{.P}}{\text{.}} \cr} $$
Now, multiply each term by $$abcd.$$
$$\frac{{abcd}}{d},\frac{{abcd}}{c},\frac{{abcd}}{b},\frac{{abcd}}{a}$$
$$abc, abd, acd, bcd$$ are in H.P.