An interesting problem (3)

A solid rubber ball rebounds to threefourths the height it is dropped from. What is the total vertical distance traveled by a ball dropped from a height of 24 feet as it bounces to rest?

24+3/4(24)(2)+(3/4^2)(24)(2)+(3/4^3)(24)(2)+.....
(The x2 is because the ball drops the same distance up and down)This is an infinite arithmetic sequence.
Let S = 3/4(24)(2)+(3/4^2)(24)(2)+... = 36+(3/4)(36)+(3/4^2)(36)+....
So 4/3S=48+36+(3/4)(36)+....
So 4/3SS=1/3S=48
So S=144
So S+24=168?