(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: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 [tex]\frac{1}{2}[/tex] foot and every jump goes [tex]\frac{1}{2}[/tex] as far as her prior jump.That means  this is a GP where [tex]a=\frac{1}{2}[/tex] and [tex]r=\frac{1}{2}[/tex]We want the sum should be 1.Now use the formula for sum of GP.[tex]s=\frac{a}{1 - r}\\ s=\frac{ \frac{1}{2}}{1-\frac{1}{2} }\\ s=\frac{ \frac{1}{2}}{\frac{1}{2}}=1[/tex]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.