Looks fine to me.
the question is:
A ball is dropped from a height of 8m. it rebounds to 3/4 of its height after each bounce. Find the total distance travelled by the ball when it touches the floor on the tenth bounce.
this is my solution
first bounce: 8
up 6 down 6 making 12 added at second bounce touch
next up and down 4.5 each making 9 added at 3rd bounce touch
Disregarding first bounce, the first term is 12 and r = 3/4 and n will equal 9
so that's 12 (1 - (3/4)^9) over (1 - 3/4) = 44.396, plus 8 = 52.396 m
See what you think