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?

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.