Question

3. An online video game tournament begins with 1024 players. Four players play in each

Answer 1

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 : $\frac{1024}{4}=256 , \frac{256}{4}=64 , \fra{64}{4}=16 , \frac{16}{4}=4 , \frac{4}{4}=1$

So, GP: 256, 64,16,4 , 1

First term = a = 256

Common ratio = $\frac{64}{256}=\frac{4}{16}=\frac{1}{4}$

Formula of nth term =$a_n=ar^{n-1}$

$1 = 256 (\frac{1}{4})^{n-1}$

$\frac{1}{256}=(\frac{1}{4})^{n-1}$

$(\frac{1}{4})^9=(\frac{1}{4})^{n-1}$

4=n-1

5=n

So, Sum of first n terms=$S_n=\frac{a(1-r^n)}{1-r}$

Substitute n = 5

$S_5=\frac{256(1-(\frac{1}{4})^5)}{1-\frac{1}{4}}$

$S_5=341$

Hence the winner play 341 games.