Question

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 1

My sister will swing the total distance = 40 feet

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 =
`(a)/((1-r))` [Since r < 1]

=
`(8)/(1-0.8)`

=
`(8)/(0.2)`

= 40 feet

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