There is a state soccer tournament with 128 teams competing for 1st place. each week, half of the teams get eliminated. how many teams remain after 6 weeks?

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Houston

Mathematics

29 October, 10:37

There is a state soccer tournament with 128 teams competing for 1st place. each week, half of the teams get eliminated. how many teams remain after 6 weeks?

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Mcintyre · Answer 1

The situation described above is an example of a geometric sequence. The common ratio is 1/2 and the initial term (a1) is 128. The second term of the sequence is the number of teams left after a week. Hence, the number after six weeks is the 7th term. To solve for the 7th term,

a7 = a1 x r^ (n - 1)

a7 = (128) x 0.5^ (6) = 2

Thus, only 2 teams remain after 6 weeks.