# Calculating Speed of Geometric Progression - Mechanics

• LagrangeEuler
In summary, the conversation is discussing the calculation of the derivative ##y′_β##, which represents the speed of a particle moving in a geometric progression. The author uses a minus sign in the derivative formula to obtain a positive quantity. This is related to the motion of the particle and can be seen on pages 4 and 5 of the provided text.
LagrangeEuler
One question. In the text

http://locomat.loria.fr/napier/napier1619construction.pdf

author calculate

##y′_β=−10^7a^t lna##
for
##y_β=10^7a^t##
(see pages 4 and 5)
why minus sign in derivative? ##y_{\beta}'## is speed. And they use minus sign as I see just to obtain positive quantity for ##y′_β=10^7a^t lna##. Is there any relation between that sign and motion of the particle? Particle moves in the some law of geometric progression.

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LagrangeEuler said:
http://locomat.loria.fr/napier/napie...nstruction.pdf

This link is not complete. It gives me a "Not Found" error in my Web browser. Could you please post a correct version of it?

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Try now.

## What is geometric progression?

Geometric progression is a sequence of numbers where each term is multiplied by a constant ratio to get the next term. For example, the sequence 2, 4, 8, 16, 32 is a geometric progression where the ratio is 2.

## How do you calculate the common ratio in a geometric progression?

The common ratio in a geometric progression can be calculated by dividing any term by the previous term. For example, in the sequence 2, 4, 8, 16, 32, the common ratio would be 2 since 4 ÷ 2 = 2, 8 ÷ 4 = 2, and so on.

## What is the formula for calculating the nth term in a geometric progression?

The formula for calculating the nth term in a geometric progression is: an = a1 * rn-1, where an is the nth term, a1 is the first term, and r is the common ratio.

## How do you find the sum of a geometric progression?

The sum of a finite geometric progression can be calculated using the formula: Sn = a1 * (1 - rn) / (1 - r), where Sn is the sum of the first n terms, a1 is the first term, and r is the common ratio. For an infinite geometric progression, the sum can be calculated using the formula: S = a1 / (1 - r), where S is the sum and r is the common ratio.

## How is geometric progression used in mechanics?

In mechanics, geometric progression is used to model the motion of an object with constant acceleration. The distance traveled by the object in each unit of time can be represented as a geometric progression, with the common ratio being equal to the acceleration. This allows for the prediction of the object's position at any given time.

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