Question 1185522: Find the missing term in harmonic sequence. Show the solution
___,1/2,2/5,1/3,___
Found 2 solutions by robertb, greenestamps:
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website!
If the numbers a, 1/2, 2/5, 1/3, b are in harmonic progression, then their reciprocals are in arithmetic progression, i.e.,
1/a, 2, 5/2, 3, 1/b
are in AP.
It is quite clear that 1/a = 3/2 and 1/b = 7/2. (The common difference is 1/2.)
===> a = 2/3 and b = 2/7.
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
The response from tutor @robertb shows one way of solving a problem like this involving harmonic sequences.
Here is a different way that I personally prefer.
In a harmonic sequence, the terms can be written with a common NUMERATOR, and with DENOMINATORS that form an arithmetic sequence.
So given the harmonic sequence
____, 1/2, 2/5, 1/3, ____
rewrite all the given terms with the same numerator:
____, 2/4, 2/5, 2/6, ____
Then the pattern is clear:
2/3, 2/4, 2/5, 2/6, 2/7
ANSWER: The missing numbers are 2/3 and 2/7
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