Question

You drop a ball from a height of 0.5 meter. Each curved path has 52% of the height of the previous path.
a. Write a rule for the sequence using centimeters. The initial height is given by the term n = 1.
b. What height will the ball be at the top of the third path?

Answer 1

a. (0.5 meter) * $0.52^{n-1}$

b. (0.5 meter) * $0.52^{3-1}$ = (0.5 meter) * $0.52^{2}$ = 0.1352 meter
    This assumes you mean "The top of the first path is the initial height of 0.5 meter" which would then use n=3 as the top of the third path.