Get expert insights and community-driven knowledge on IDNLearn.com. Our community provides accurate and timely answers to help you understand and solve any issue.
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
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.
