Question 1163968: Question: “Find the 8th term of the harmonic sequence 2/3, ½, 2/5 …” (Quotation marks are mine)
I don’t need the answer. It is 1/5. I solved it after lots of frustration! I just need some clarification of mathematical wording and conventions that I should be familiar with.
Frustration:
I know the definition of harmonic sequence and the meaning of it being the inverse of an arithmetic sequence and all.
But, when they say explicitly “harmonic sequence 2/3, ½, 2/5 …” shouldn’t I assume that those three terms are already inverted. Why do I have to invert them? In other words, what wording will prompt me to know that they are being presented after the inversion or prior to inversion? Shouldn't the above problem be worded as "Find the 8th term of the harmonic sequnce of the following NUMBERS...".
Thank you
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
As you say, the terms of a harmonic sequence are the reciprocals of the terms of an arithmetic sequence. So the terms of the arithmetic sequence are "inverted" to get the terms of the harmonic sequence.
So the given terms ARE the inverted terms OF THE ARITHMETIC sequence.
To solve the problem, you invert the given terms to find the terms of the arithmetic sequence; when you get to the 8th term of the arithmetic sequence, you invert it to find the 8th term of the harmonic sequence.
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