Using a geometric sequence, it is found that after 3 rounds, 8 teams are left.
In a geometric series, the quotient between consecutive terms is always the same, and it is called common ratio q.
The general equation of a geometric series 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 number of teams after 3 rounds is the 4th term of sequence, as the first is the initial number(0 rounds), thus:
[tex]a_n = a_1q^{n-1}[/tex]
[tex]a_4 = 64\left(\frac{1}{2}\right)^{4-1}[/tex]
[tex]a_4 = 8[/tex]
After 3 rounds, 8 teams are left.
A similar problem is given at https://brainly.com/question/25317689
