Question

5/28

Answer 1

Answer:

Part a) The rule of the sequence is $A(n)=50(0.52^{n-1})$

Part b) The height of the ball will be $13.52\ cm$

Step-by-step explanation:

Part a) Write a rule for the sequence using centimeters. The initial height is given by the term n = 1.

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant called the common ratio (r)

In this problem we have a geometric sequence

Let

n-----> the number of path

a1 ----> is the initial height

r -----> the common ratio

we have

$a1=0.5\ m=0.5*100=50\ cm$

$r=52\%=52/100=0.52$

The rule for the sequence is equal to

$A(n)=a1(r^{n-1})$

substitute

$A(n)=50(0.52^{n-1})$

Part b) What height will the ball be at the top of the third path?

For n=3      

substitute in the equation

$A(3)=50(0.52^{3-1})$  

$A(3)=50(0.52^{2})$

$A(3)=13.52\ cm$