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A ball is dropped from a height of 20 feet. Each time it bounces, it reaches â…“ of its previous height. What is the total vertical distance the ball has traveled when it hits the ground the fourth time?

Respuesta :

Edufirst
You have to calculate the sum of 20 + 20/3 + 20/ 9 + 20/27 + 20/ 81 + ...

That is a geometric series with first term 20 and r = 1/3.

Now you can use the formula for the sum of a geometric series:

∑ Ai from i = 0 to i = A / ( 1 - r), where A is the first term.

=> 20 + 20/3 + 20/ 9 + 20/27 + 20/ 81 + ... = 20 / ( 1 - 1/3) = 20 / (2/3) = 20*3/2 = 30.

Answer: 30 feet.

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