SOLUTION: A pendulum bob swings through an arc 70 inches long on its first swing. Each swing, thereafter, it swings only 89% as far as on the previous swing. What is the length of the arc

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Question 46789: A pendulum bob swings through an arc 70 inches long on its first swing. Each swing, thereafter, it swings only 89% as far as on the previous swing. What is the length of the arc after 9 swings?
Round your answer to two decimal places, if necessary.
I need to know how to set this problem up please. I get mixed up when trying to set it up and then become completely frustrated! Please help!
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the nth swing is 0.89 times the length of the (n-1)th swing.
Let the length of the nth swing be L%5Bn%5D.
L%5B1%5D=70
L%5B2%5D=0.89%2870%29
L%5B3%5D=0.89%280.89%2870%29%29=0.89%5E2%2870%29
L%5B4%5D=0.89%280.89%280.89%2870%29%29%29=0.89%5E3%2870%29
See a pattern emerging yet?
The formula for the length of the nth swing is L%5Bn%5D=70%280.89%5E%28%28n-1%29%29%29
So The length of the 9th swing is......
L%5B9%5D=70%280.89%5E8%29
which is 27.56 inches, to 2 decimal places.

I hope this helps,
Adam
P.S. please visit my website, it may be helpful to you. The address is www.geocities.com/quibowibbler