Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Using a geometric sequence, it is found that the rule for the number of matches played in the nth round is given by:
[tex]a_n = 64\left(\frac{1}{2}\right)^n[/tex]
The rule makes sense for values of n of at most 6, as in the last round, which is the 6th and final round, 1 game is played.
What is a geometric sequence?
A geometric sequence is a sequence in which the result of the division of 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, we have that:
- In the first round of the tournament, 64 matches are played, hence the first term is [tex]a_1 = 64[/tex].
- In each successive round, the number of matches played decreases by one half, hence the common ratio is [tex]q = \frac{1}{2}[/tex].
Thus, the rule is:
[tex]a_n = 64\left(\frac{1}{2}\right)^n[/tex]
The last round is the final, in which 1 game is played, hence:
[tex]1 = 64\left(\frac{1}{2}\right)^n[/tex]
[tex]\left(\frac{1}{2}\right)^n = \frac{1}{64}[/tex]
[tex]\left(\frac{1}{2}\right)^n = \left(\frac{1}{2}\right)^6[/tex]
[tex]n = 6[/tex]
Hence, the rule makes sense for values of n of at most 6, as in the last round, which is the 6th and final round, 1 game is played.
More can be learned about geometric sequences at https://brainly.com/question/11847927
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
