A ball is thrown upward to a height of h 0 meters. After each bounce, the ball rebounds to a fraction r of its previous height. Let h n be the height after the nth bounce and let S n be the total...

A ball is thrown upward to a height of h₀
meters. After each bounce, the ball rebounds to a fraction r of its previous height. Let h_n
be the height after the nth bounce and let S_n
be the total distance the ball has traveled at the moment of the nth bounce.

a. Find the first four terms of the sequence {S_n}.

b. Make a table of 20 terms of the sequence {S_n} and determine a plausible value for the limit of {S_n}.

1. h₀
= 20, r = 0.5

2. h₀
= 20, r = 0.75