Chapter 9, Problem 58SGR

To determine

Draw a graph to represent the situation.

Answer to Problem 58SGR

The GP series is: $20,10,5,2.5,1.25,\mathrm{0.625.....}$

Explanation of Solution

Given:

A basketball is dropped from a height of 20 feet. It bounces to 1.2 its height after each bounce. Draw a graph to represent the situation.

Concept Used:

The ball loses $\frac{1}{2}$ its height after each bounce; hence it forms a geometric sequence. To determine a term (height after each bounce) multiply the previous term by $\frac{1}{2}$ .

Calculation:

The ball loses $\frac{1}{2}$ its height after each bounce; hence it forms a geometric sequence. To determine a term (height after each bounce) multiply the previous term by $\frac{1}{2}$ .

Initial height is the first term = 20 feet.

Find the next few terms of the series to get the series.

1^st term: $a_1=20$ and the common difference is $\frac{1}{2}$

2^nd term: $a_2=a_1·r=20·\frac{1}{2}=10$ ; 3^rd term: $a_3=a_2·r=10·\frac{1}{2}=5$

4^th term: $a_4=a_3·r=5·\frac{1}{2}=2.5$ ; Fifth term: $a_5=a_4·r=2.5·\frac{1}{2}=1.25$

6^th term: $a_6=a_5·r=1.25·\frac{1}{2}=0.625$

The GP series is: $20,10,5,2.5,1.25,\mathrm{0.625.....}$

The graph of the situation:

  

Thus, the GP series is: $20,10,5,2.5,1.25,\mathrm{0.625.....}$