Question

solve in each situation. you may use a calculator and round your answer to the nearest tenth of a unit when necessary.

1. a ball is dropped from a height of 500 meters. the table shows the height of each subsequent bounce. the heights form a geometric sequence. how high does the ball bounce on the \\(4^{\text{th}}\\) bounce? round your answer to the nearest tenth of a meter.

first, identify each term in the sequence. for this sequence,
\\f(1) = \square, \quad f(2) = \square, \quad f(3) = \square \quad \text{and} \quad f(4) = \square\\

then, find the common ratio \\(r\\).
\
= \frac{\square}{\square} = \square\\

to find the term \\(f(4)\\), repeatedly multiply the common ratio \\(r = \square\\).

Explanation:

Identify the sequence terms

Using the Geometric Sequence Terms and Geometric Sequences knowledge points

$$
LATEXBLOCK0
$$

Find the common ratio

Using the Common Ratio knowledge point

$$ r = \frac{f(2)}{f(1)} = \frac{400}{500} = \frac{4}{5} = 0.8 $$

Calculate the fourth term

Using the Geometric Sequence Terms knowledge point

$$ f(4) = f(3) \cdot r = 320 \cdot 0.8 = 256 $$

Answer:

First, identify each term in the sequence. For this sequence,
\(f(1) =\) <blank>500</blank>, \(f(2) =\) <blank>400</blank>, \(f(3) =\) <blank>320</blank>, and \(f(4) =\) <blank>256</blank>.

Then, find the common ratio \(r\).
\(r =\) <blank>\(\frac{400}{500}\)</blank> \(=\) <blank>\(0.8\)</blank>

To find the term \(f(4)\), repeatedly multiply the common ratio \(r =\) <blank>\(0.8\)</blank>.