Question

(Riddle)

An athlete is able to jump FOREVER. However, everytime that she jumps she gets a bit more tired, and every jump goes 12 as far as her prior jump. Now, for her very first jump, she goes 12 of a foot.


On her second jump, she goes 14 of a foot, and so on and so forth. The beginning of her journey is shown in the gif below.


How many jumps does it take for her to travel 1 foot?

Answer 1

Answer:

The athlete will never reach one foot because they only ever jump half of the remaining distance.

Step-by-step explanation:

Consider the provided information.

It is given that on her first jump she goes $\frac{1}{2}$ foot and every jump goes $\frac{1}{2}$ as far as her prior jump.

That means  this is a GP where $a=\frac{1}{2}$ and $r=\frac{1}{2}$

We want the sum should be 1.

Now use the formula for sum of GP.

$s=\frac{a}{1 - r}\\ s=\frac{ \frac{1}{2}}{1-\frac{1}{2} }\\ s=\frac{ \frac{1}{2}}{\frac{1}{2}}=1$

Hence the maximum value is One Foot.

That means she has to take infinite number of steps to complete a distance of 1 foot.

Therefore, the athlete will never reach one foot because they only ever jump half of the remaining distance.

Answer 2

Answer:

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Step-by-step explanation: