AMC / AIME · Geometric Sequences · Hard

Geometric Sequences: A ball rebounds to math of its height. Dropped from math, find fourth-bounce height.

Common ratios.

Try the problem

A ball rebounds to 3/43/4 of its height. Dropped from 6464, find fourth-bounce height.

Hint and answer

Concept to use

Infinite $|r|<1$.

Hint

Use ratios for terms and the finite or infinite geometric-sum formula.

Answer

81/4

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