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The four positive numbers a,b,c,d are in arithmetic progression.What is the progression sequence of abc,abd,bcd? I found out the common difference b-a,c-b.. but that does not seem to be of much use.

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If $a,b,c,d$ are in Arithmetic Progression, dividing each term of an AP by a non-zero term still results in an AP, hence dividing with $abcd$ will still yield an AP.

Hence, $\frac{1}{bcd},\frac{1}{acd},\frac{1}{abd},\frac{1}{abc}$ are in AP.

So, the terms $abc,abd,acd,bcd$ are in HP. It might be a typo, but the sequence you have mentioned is not an HP.