Answers

2014-11-20T22:51:40+08:00
See attachment for illustration
Let a1 be 2/3(50) = 100/3
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Since this is in infinite geometric progression then we'll use
S_n =  \frac{a_1}{1-r}
where r is the common ratio 
S_n=\frac{100/3}{1- \frac{2}{3} }
S_n = 100
Since the distance traveled by the ball is twice 2/3 of the previous then we'll have Sn multiplied by 2
S_n = 100(2)
S_n = 200 ft
But remember that we have not included the initial 50ft distance traveled since a1 is 2/3 of 50.
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Total distance traveled by the ball then is 
d_{total} = 200 + 50
d_{total} = 250ft
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