Answer:
The winner play 341 games.
Step-by-step explanation:
An online video game tournament begins with 1024 players.
Four players play in each game
It forms GP : [tex]\frac{1024}{4}=256 , \frac{256}{4}=64 , \fra{64}{4}=16 , \frac{16}{4}=4 , \frac{4}{4}=1[/tex]
So, GP: 256, 64,16,4 , 1
First term = a = 256
Common ratio = [tex]\frac{64}{256}=\frac{4}{16}=\frac{1}{4}[/tex]
Formula of nth term =[tex]a_n=ar^{n-1}[/tex]
[tex]1 = 256 (\frac{1}{4})^{n-1}[/tex]
[tex]\frac{1}{256}=(\frac{1}{4})^{n-1}[/tex]
[tex](\frac{1}{4})^9=(\frac{1}{4})^{n-1}[/tex]
4=n-1
5=n
So, Sum of first n terms=[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Substitute n = 5
[tex]S_5=\frac{256(1-(\frac{1}{4})^5)}{1-\frac{1}{4}}[/tex]
[tex]S_5=341[/tex]
Hence the winner play 341 games.
