Let the positive numbers a , b , c , d be in A.P. Then a b c , a b d , a c d , b c d are [2001]

Question

Let the positive numbers $a, b, c, d$ be in A.P. Then $a b c, a b d, a c d, b c d$ are [2001]

Smart Achievers · Accepted Answer

(4)

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

$\Rightarrow \frac{d}{a b c d}, \frac{c}{a b c d}, \frac{b}{a b c d}, \frac{a}{a b c d} are also in A.P.$

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

$∴$ $a b c, a b d, a c d, b c d are in H.P.$

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