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Sagot :
Using a geometric sequence, it is found that:
- The rule for the height of the nth bounce is:
[tex]a_n = 52(0.65)^{n-1}[/tex]
- The height of the fifth bounce is of 9.28 cm.
In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem:
- Bounces to 65% of the height from which it was dropped, thus the common ratio is of [tex]q = 0.65[/tex].
- Dropped from 80 cm, thus, the height of the first bounce is [tex]a_1 = 80(0.65) = 52[/tex].
Thus, the rule for the height of the nth bounce is:
[tex]a_n = 52(0.65)^{n-1}[/tex]
The height of the fifth bounce is [tex]a_5[/tex], thus:
[tex]a_5 = 52(0.65)^{5-1} = 9.28[/tex]
The height of the fifth bounce is of 9.28 cm.
A similar problem is given at https://brainly.com/question/11847927
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