Question

A frog starts jumping from the middle of a circular pond.

The pond is 12 metres across, from one side to the other.
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The frog always jumps half the distance left to the edge of the pond.
How far is the frog from the edge after 3 jumps?

Answer 1

Explanation:

Remark

You could do this simply by taking 3 jumps, without using a formula. That would work as well, but I think it is easier just to make 3 jumps.

Jump One

The frog starts out 6 meters from an edge. (He/she starts at the middle). The frog makes 1 jump.

He lands 3 meters (1/2 the distance) from the edge.

Jump Two

He jumps in such a way that he is 1/2 the distance from the edge. So far he is 3 meters away. His jump puts him 1 1/2 meters from the edge.

Jump Three

The frog makes one last jump. It is 1 1/2 meters from the edge. The third jump takes it 1/2 * 3/2 = 3/4 a meter away from the edge.

Answer: 3/4 of a meter from the edge.