Is the answer 72? Kinda confused.

[keen meadow]

So I set 9 = a_1 and (7/8) = r then, because (7/8) is less than one, I know that the ball converges to a point so I used the formula a/1-r and got 72. Just want to double check my work and may sure my thinking is one the right track. Would appreciate any clarifications.

[jagged sandal]

e

[obtuse cobalt]

Keep in mind the ball travels 9(7/8)^r distance twice for each r>=1 because it bounces up to that height then falls back down from that height

[keen meadow]

would i just need to multiply 72 by 2?

[obtuse cobalt]

Almost. The ball starts at 9m high but it does not ever travel upwards 9m so you will need to subtract 9 from 72*2 to account for that

[keen meadow]

But how about when it travels down for the first time? does that not count towards the total distance the ball traveled?

[obtuse cobalt]

Yeah it does, that is why we only subtract 9 instead of 18. In total it looks something like this:

solution = 9 + 9(7/8) + 9(7/8) + 9(7/8)^2 + 9(7/8)^2 + ...

And we know 9 + 9 + 9(7/8) + 9(7/8) + 9(7/8)^2 + 9(7/8)^2 + ... = 2(9 + 9(7/8) + 9(7/8)^2 + ...) = 2(72)

So we need to subtract 9 from this to get the solution

[keen meadow]

Ohhhh that makes sense