A ball is dropped from a height of 11 feet and bounces.Each bounce is $\frac{2}{3}$ of the height of the bounce before.Find an expression for the height to which the ball rises after it hits the floor for the n^thtime. A) $11\left(\frac{2}{3}\right) \cdot n$ B) $11\left(\frac{2}{3}\right)^{n}$ C) $11\left(1-\left(\frac{2}{3}\right)^{n}\right)$ D) $\frac{11\left(1-\left(\frac{2}{3}\right)^{n}\right)}{1-\frac{2}{3}}$

Question

Quizplus · Accepted Answer

The height of the ball after the nth bounce can be represented by a geometric sequence where the first term is 11 (the initial height) and the common ratio is $\frac{2}{3}$ (since each bounce reaches $\frac{2}{3}$ of the height of the previous bounce). The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$, but since we are looking for the height after the ball hits the floor for the nth time, we use $n$ instead of $n-1$, resulting in $11\left(\frac{2}{3}\right)^{n}$.

A Ball Is Dropped from a Height of 11 Feet 23\frac{2}{3}32​

A Ball Is Dropped from a Height of 11 Feet $\frac{2}{3}$