Tournament Brackets
First round: 64 teams, 32 games
Second round: 32 teams, 16 games
Third round: 16 teams, 8 games
Fourth: 8 teams, 4 games
Fifth round: 4 teams, 2 games
Sixth round: 2 teams, 1 game
Which geometric series should you use to find the total number of games played?
21
helpfulIn the first round of the tournament, 32 games are played.
In each successive round, the number of games played decreases by 1/2.
We know;
a(n) = a • r^(n−1)
a = 32
r = 32/64 = 1/2
So, we get;
The rule for the number of games played in the nth round is given by:
a(n) = 32 • (½)^n - 1
where 1 ≤ n ≤ 6
Thus, the correct option is :
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