The frog's jump represent a geometric series.
The sum of finite geometric series can be solved using the equation:
Sn = ao ( (1-r^n)/(1-r) )
Plugging in the values,
S8 = 1 ( (1-2^8)/(1-2) )
S8 = 255
Therefore, after 8 hops, the frog will have traveled 255 inches
