Answer: The first 5 times are 256 , 128 , 64 , 32 and 16
Step-by-step explanation:
The situation is a scenario of Geometric sequence. The nth term for a geometric sequence is given as:
[tex]t_{n}[/tex] = a[tex]r^{n-1}[/tex]
a = 256
r =1/2
substituting into the formula
when n = 1
[tex]t_{1}[/tex] = 256([tex](1/2)^{1-1}[/tex])
[tex]t_{1}[/tex] = 256
when n = 2 ,this is the second round , we have
[tex]t_{2}[/tex] = 256 x [tex]\frac{1}{2} ^{2-1}[/tex]
[tex]t_{2}[/tex] = 128
When n = 3 , we have
[tex]t_{3}[/tex] = 256 x 1/4
[tex]t_{3}[/tex] = 64
when n = 4
[tex]t_{4}[/tex] = 256 x 1/8
[tex]t_{4}[/tex] = 32
when n = 5
[tex]t_{5}[/tex] = 256 x 1/16
[tex]t_{5}[/tex] = 16
Therefore the first five terms of the sequence that represent the number of games in each round of the tournament are:
256 , 128 , 64 , 32 , 16
