SOLUTION: A sequence of numbers is said to form a harmonic progression provided their reciprocals form an arithmetic progression. Insert three harmonic means between

SOLUTION: A sequence of numbers is said to form a harmonic progression provided their reciprocals form an arithmetic progression. Insert three harmonic means between - 1/2 and 1/14.

Question 922288: A sequence of numbers is said to form a harmonic progression provided their reciprocals form an arithmetic progression. Insert three harmonic means between - 1/2 and 1/14.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I understand the first term to be the positive number .
We need an arithmetic progression, where each term differs from the one before by a common difference .
The first term is , which is followed by 3 more terms, and then by .
The terms are , , , ,
The fifth term is .
--->--->--->---> .
So the terms of the arithmetic progression are
, , , , ,
and the terms of the harmonic progression are
, , , , and .

NOTE: If the first term was ,
then the arithmetic progression would be
, , , , ,
and the harmonic progression would be
, , , , .
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