Question

7. The new York Volleyball Association

Answer 1

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:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

In this problem:

• 64 teams were invited, thus $a_1 = 64$.
• After each round, half the teams are eliminated, thus $q = \frac{1}{2}$.

The number of teams after 3 rounds is the 4th term of sequence, as the first is the initial number(0 rounds), thus:

$a_n = a_1q^{n-1}$

$a_4 = 64\left(\frac{1}{2}\right)^{4-1}$

$a_4 = 8$

After 3 rounds, 8 teams are left.

A similar problem is given at brainly.com/question/25317689