Question 1196696: Insert the indicated number of harmonic means given the first and last terms.
5/2 and 5/27
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The post does not specify the number of harmonic means.
But inserting harmonic means between two given numbers is a simple process, performed as follows:
(1) take the reciprocals of the two given numbers;
(2) insert the specified number of ARITHMETIC means between those two numbers; and
(3) take the reciprocals of those arithmetic means to get the harmonic means
The reciprocals of the two given numbers are 2/5 and 27/5; the difference between those two numbers is 25/5 = 5. So one easy problem is to divide that difference into 5 equal parts, which means inserting 4 arithmetic means:
2/5, 7/5, 12/5, 17/5, 22/5, 27/5
Then the harmonic sequence is with the reciprocal of those numbers:
5/2, 5/7, 5/12, 5/17, 5/22, 5/27
So if the problem was to insert 4 harmonic means between the two given numbers, then those 4 harmonic means are
5/7, 5/12, 5/17, and 5/22
If the specified number of harmonic means was not 4, then a similar process would be followed -- but the numbers would not be as "nice".
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