Answer
A situation in everyday life that can be modeled by an infinite geometric series is playing a swing in the park in calculating the total height attained for all the swings before the swing comes to a complete stop.
Work Step by Step
A situation in everyday life that can be modeled by an infinite geometric series is playing a swing in the park in calculating the total height attained for all the swings before the swing comes to a complete stop.
Suppose the initial height reached by a kid for the first swing is 6 feet above the ground and for each of the subsequent height attained after he completed a swing, the height falls to $\frac{3}{4}$ of the previous one.
The total height he attained during all his swings before the swing comes to a complete stop is equal to the total sum of all the terms of the infinite geometric series with $a_{1} = 6$ and $r = \frac{3}{4}$ whose general term $a_{n} = 6(\frac{3}{4})^{n - 1}$ with n = number of swings in the series.
The total height attained for all his swings before the swing comes to a complete stop is equal to $\frac{6}{1 - \frac{3}{4}}$
= $24$ feet
