Question

A frog is hopping along in a straight line. Each hop is twice as far as its previous hop. Its first hop covers 1 inch. After 8 hops, the frog will have traveled _____ inches.

Answer 1

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