SOLUTION: Insert the indicated number of harmonic means given the first and last terms. Show the solution. 1/2 and 1/6 [3] or insert 3 2/3 and 2/9 [2] or insert 2 5/2 and 5/2

Algebra ->  Sequences-and-series -> SOLUTION: Insert the indicated number of harmonic means given the first and last terms. Show the solution. 1/2 and 1/6 [3] or insert 3 2/3 and 2/9 [2] or insert 2 5/2 and 5/2      Log On


   

Question 1185523: Insert the indicated number of harmonic means given the first and last terms. Show the solution.

1/2 and 1/6 [3] or insert 3
2/3 and 2/9 [2] or insert 2
5/2 and 5/27 [4] or insert 4
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

I will do the first progression only-- insert 3 harmonic means between 1/2 and 1/6.
If five numbers are in harmonic progression then their reciprocals are in arithmetic progression.
Let those numbers in AP be 2, a, b, c, 6.
Then it's quite clear that the numbers in between are 2, red%283%29,+red%284%29, red%285%29, 6.
Therefore the three harmonic means between 1/2 and 1/6 are 1/3, 1/4, and 1/5.