Question

6. Write the explicit formula for the geometric sequence of the height of the ball on the 10th bounce.First bounce: 54 inchescommon ratio: 0. 750

Answer 1

The height of the ball initially is 54 inches. The common ratio has been provided which is 0.750.

The explicit formular for the geometric sequence is shown as;

$\begin{gathered} ar^{n-1} \\ \text{Where a is the first term in the sequence,} \\ r\text{ is the common ratio betw}een\text{ every successive term} \\ \text{And n is the nth term} \\ \text{The explicit formular for the height of the ball on the 10th bounce is;} \\ ar^{n-1} \\ 54\times(0.750)^{10-1} \\ 54\times(0.750)^9 \\ 54\times0.07508468\ldots \\ 4.0545 \end{gathered}$

The explicit formula is shown as;

54 x (0.750)^9

The rest is simply to solve for the height on the 10th bounce