Question

A wrestling tournament begins with 128 competitors. In the first round, each competitor has 1 match against another wrestler. The winner of each match moves on to the next round until there is a winner. Write a sequence in which the terms represent the number of players still in the tournament at the end of each round. Describe the sequence? How many rounds are in the tournament?

Answer 1

Answer:

7 rounds were played.

Step-by-step explanation:

A wrestling tournament begins with 128 competitors. In every round competitor has 1 match against another wrestler and winner moves to the next round. We have to construct a sequence representing all rounds of this tournament.

In first round total matches played = 128/2 = 64

In second round number of matches played = 64/2 = 32

In third round matches played = 32/2 = 16

Similarly all the rounds were played.

Now we get the sequence as 64, 32, 16, 8, 4, 2, 1

This sequence is a geometric sequence having first term 64

Common factor = 32/64 = 1/2

Number of terms = 7

Explicit rule $a_{n}= a(r)^{n-1}=64.(\frac{1}{2})^{n-1}$

Total seven rounds were played.

Answer 2

Theres 64 rounds i think that the correct answer