Harmonic-geometric progression

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Harmonic and geometric progressions are distinct mathematical sequences, with harmonic progression defined as Tn = 1/n and geometric progression as Tn = a * r^n. The formula Tn = a + d(n-1) represents an arithmetic progression, not harmonic or geometric. The discussion highlights confusion regarding the classification of these sequences, with a mention of Gauss's work on arithmetic-geometric progressions, which possess unique mathematical properties. There is no established concept of arithmetic-harmonic progression in standard mathematics. Further clarification and examples are anticipated from participants in the discussion.
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Can anyone explain to me the concept and the application of the harmonic-geometric progression?

T sub n = a + d(n-1)

Thanks!

:smile:
 
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I have no idea where you got this. There ARE "harmonic" progression (Tn= 1/n) and geometric progressions (Tn= a rn) but the example you give Tn = a + d(n-1) is neither one, it is an "arithmetic" progression.
 
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Gauss worked with arithmetic-geometric progressions. I'm not sure what they "mean" but they have nice mathematical properties. When I get back to my books I'll post something on these. But arithmetic-harmonic I've never heard of.
 
RE

got it from my profe HallsofIVy
 

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