Question 600139: Karen tees up on the 9th hole at a golf course for a 200 yard hole. She makes an initial drive (first shot) directly toward the hole. Her second shot travels 50 yards. Karen's third shot travels 25 yards, her fourth 12.5 yards, and so on in this pattern. Assume that the first shot fits the pattern and that the ball continues directly toward the hole on each shot.
Find the first shot less than 10 yards from the hole and the first shot less than 5 yards from the hole? Find the distance covered by the ball. Will the ball travel 200 yards? Explain why or why not. Use two different methods to justify your reasoning.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! This is a geometric sequence with terms 100,50,25,12.5,...
The sum of a geometric sequence is S(n) = a(1-r^n)/(1-r) where r=common ratio and a=the 1st term
Here the common ratio is 50/100 = 1/2
For the ball to 10 yds from the hole, it has covered a distance of 190 yds,
so S(n) = 190
190 = 100(1-(1/2)^n)(1-(1/2))
Solve for n using logarithms -> n = 4.32
So after the 5th shot, the ball is less than 10 yds from hole
For 5 yds from the hole, solve the above with S(n) = 195
This gives n = 5.32
So after the 6th shot, the ball is < 5 yds away
In theory, the ball never covers the full 200 yds, since the remaining distance, while getting very small, is always non-zero.
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