You've only counted the downward drops. You also need to count the upward bounces, which will be another geometric series with a = 8, r = 0.4 and n = 6.
A tennis ball is dropped from a height of 20 m and bounces to 40% of its previous height on each bounce. The total vertical distance travelled is made up of the upward bounces and downward drops. What is the total vertical distance for the 6th time?
My attempt:
t1 = 20 cm
r = 0.40
n = 6
Sn = t1r^n - 1 / r - 1
S6 = 20(0.40^6 - 1) / 0.40 - 1
S6 = -19.91808 / -.6
S6 = 33.1968
The correct answer is 46.6 m and I don't know how I can get that, any help would be appreciated!