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Sagot :
Using a geometric sequence, it is found that 7 rounds must be scheduled in order to complete the tournament.
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, the first round has 128 players, and each round, the players who lose a game go home, hence the common ratio is of q = 0.5.
Then, the geometric sequence for the number of players after n rounds is given by:
[tex]a_n = 128(0.5)^n[/tex]
In the final round, there is one player, hence:
[tex]1 = 128(0.5)^n[/tex]
[tex](0.5)^n = \frac{1}{128}[/tex]
[tex](0.5)^n = \left(\frac{1}{2}\right)^7[/tex]
n = 7
7 rounds must be scheduled in order to complete the tournament.
More can be learned about geometric sequences at https://brainly.com/question/11847927
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