Math CentralQuandaries & Queries


Subject: Math story problems
Name: Leah
Who are you: Student

Rebecca's little sister liked for her to push her in the swing at the park. The other day Rebecca pulled the swing back and let it go. She would have kept pushing, but she suddenly saw a friend at the other end of the park. The swing traveled a total distance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped.

how do i solve this using the formula a(sub)n=a(sub)1*r to the power of n-1?

Please Help!

Hi Leah,

The first swing went 10 feet and then the second swing went 80% of 10 feet so that is

10 x 0.8 feet

The third swing went 80% of the length of the second swing so that is

(10 x 0.8) x 0.8 = 10 x 0.82 feet

The fourth swing went 80% of the third swing so that is

(10 x 0.82 ) x 0.8 = 10 x 0.83 feet

Now you should be able to see the pattern. The length of the nth swing is

10 x 0.8n-1 feet

Hence the sum of the lengths of the first swing, the second swing, the third swing, ... the nth swing is

10 + 10 x 0.8 + 10 x 0.82 + ... + 10 x 0.8n-1 feet.

Can you see how to complete the problem now?

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