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You push your younger sister on a swing one time and then allow your sister to

swing freely. On the first swing, your sister travels a distance of 8 feet. On each

successive swing, your sister travels 80% of the distance of the previous swing.

What is the total distance your sister swings?

Answer :

Answer:

My sister will swing the total distance = 40 feet

Step-by-step explanation:

On the first swing my sister travels a distance of 8 feet.

In every successive swing she travels 80% of the distance of the previous distance.

So the sequence formed by the distance traveled in every swing will be a geometric sequence.

First term of the sequence 'a' = 8 feet

common ratio 'r' = 0.80

Since this sequence is an infinite geometric sequence,

Sum of this sequence = [tex]\frac{a}{(1-r)}[/tex]  [Since r < 1]

                                     = [tex]\frac{8}{1-0.8}[/tex]

                                     = [tex]\frac{8}{0.2}[/tex]

                                     = 40 feet

Therefore, my sister will cover the total distance = 40 feet

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