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never [62]
3 years ago
11

5/28

Mathematics
1 answer:
natulia [17]3 years ago
4 0

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 <u>Geometric Sequence</u> 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

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