Question

Select the sequences that ara 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?.

A)18, 36, 54, 72, …
B)4.1, 8.2, 16.4, 32.8, …
C)–7, 14, –28, 56, …
D)980, 784, 627.2, 501.76, …
E)5, 2, –1, –4, …"

Answer 1

The correct sequence representing the number of players left after each round in a wrestling tournament starting with 128 competitors would show the numbers halving each time, creating a geometric sequence until only one winner is left after 7 rounds.

Step-by-step explanation:

To create a sequence that represents the number of players still in the tournament at the end of each round, we must halve the number of competitors at the end of each round because in every match, one wrestler wins and moves on, and one wrestler is eliminated. Starting with 128 competitors, the sequence is as follows:

1. 64 (after the first round, as half of the competitors are eliminated)
2. 32 (after the second round, half of the remaining competitors are eliminated)
3. 16 (after the third round)
4. 8 (after the fourth round)
5. 4 (after the fifth round)
6. 2 (after the sixth round)
7. 1 (after the seventh round, leaving us with the winner)

This is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio, in this case, 1/2 (or halving the term). So the tournament will have 7 rounds in total.