# Harmonic-geometric progression

• Integral0
In summary, the concept of harmonic-geometric progression is not a common one and is not a combination of harmonic and geometric progressions. It may have been used by Gauss, but its meaning is unclear and requires further research. It is not to be confused with arithmetic-harmonic progression.
Integral0
Can anyone explain to me the concept and the application of the harmonic-geometric progression?

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

Thanks!

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

## 1. What is a Harmonic-geometric progression?

A Harmonic-geometric progression is a type of mathematical sequence where each term is the product of the previous term and a constant ratio between the reciprocals of the terms.

## 2. How is a Harmonic-geometric progression different from a regular geometric progression?

In a regular geometric progression, each term is the product of the previous term and a constant ratio. In a Harmonic-geometric progression, the constant ratio is between the reciprocals of the terms, making it a more complex type of sequence.

## 3. What is the formula for finding the nth term in a Harmonic-geometric progression?

The formula for finding the nth term in a Harmonic-geometric progression is an = a1 * rn-1 / (1 + (n-1)d), where a1 is the first term, r is the common ratio, and d is the constant difference between the reciprocals of the terms.

## 4. What are some real-life applications of Harmonic-geometric progression?

Harmonic-geometric progression can be used in various fields such as finance, physics, and biology. In finance, it can be used to model compounding interest rates. In physics, it can be used to model the decay of radioactive materials. In biology, it can be used to model population growth.

## 5. How is the convergence of a Harmonic-geometric progression determined?

The convergence of a Harmonic-geometric progression is determined by the value of the common ratio, r. If r is greater than 1, the progression will diverge to infinity. If r is between 0 and 1, the progression will converge to a finite value. If r is equal to 1, the progression will converge to 1.

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