# Arithmetic Sequence.

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#### foreverbrokenpromises

A super ball is dropped from a height of 64 feet. Each time it hits the ground, it rebounds 78% of the distance it has fallen. In theory how far will the ball travel before coming to rest? Explain your method and reasoning.

so Ive tried a couple of equations/functions/ways to get this and it doesnt seem to be working. Can someone explain to me, how to start off? What to think about?

And then how to get the answer?

Thanks.

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#### dwsmith

MHF Hall of Honor
A super ball is dropped from a height of 64 feet. Each time it hits the ground, it rebounds 78% of the distance it has fallen. In theory how far will the ball travel before coming to rest? Explain your method and reasoning.

so Ive tried a couple of equations/functions/ways to get this and it doesnt seem to be working. Can someone explain to me, how to start off? What to think about?

And then how to get the answer?

Thanks.
Lets think what is happening.

$$\displaystyle t=0; h=64$$
$$\displaystyle t=1; h=64*.78$$
$$\displaystyle t=2; h=64*.78*.78=64*.78^2$$
....

$$\displaystyle 64\sum_{t=0}^{\infty}\left(\frac{39}{50}\right)^t$$

This is a geometric series which can be solved:
$$\displaystyle a\sum_{n=0}^{\infty}\left(\frac{p}{q}\right)^n=\frac{a}{1-\frac{p}{q}}$$ and $$\displaystyle \frac{p}{q}<1$$

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