Question

A regional soccer tournament has 64 participating teams. In the first round of the tournament, 32 games are played. In each successive round, the number of games played decreases by 1/2. Find a rule for the number of games played in the nth round, then find the total number of games played in the regional soccer tournament.

Answer 1

Answer:

A regional soccer tournament has 64 participating teams.

In the first round of the tournament, 32 games are played.

In each successive round, the number of games played decreases by 1/2.

Part A:

We know;

$a_n=a_1\times r^{n-1}$

$a_1=32$

$r=\frac{-1}{2}$

So, we get;

The rule for the number of games played in the nth round is given by:

$a_n=32(\frac{1}{2})^{n-1}$

where $1\leq n\leq 6$

Part B:

As in each successive round the rounds are decreasing by 1/2 we have.

round 1 = 32

round 2 = 16

round 3 = 8

round 4 = 4

round 5 = 2

round 6 = 1

So, the total number of games played in the regional soccer tournament are: $32+16+8+4+2+1=63$