Question

The number of players in a tennis tournament is reduced by half (50%) after every round. In round 1 there are 256 player, in round 2 there are 128 players, and so on. Which explicit formula models this situation? How many player compete in round 7?
I NEED HELP PLEASE

Answer 1

Answer:

$a_{n} = a_{1} (\frac{1}{2} )^{n - 1}$ where $a_{1} = 256$.

The number of players compete in round 7 will be 4.

Step-by-step explanation:

The number of players in a tennis tournament is reduced by half (50%) after every round. In round 1 there are 256 players, in round 2 there are 128 players, and so on.

So, the number of players is multiplied by $\frac{1}{2}$ gives the number of players in the next round.

Therefore, the explicit function of number of players in nth round is given by  

$a_{n} = a_{1} (\frac{1}{2} )^{n - 1}$ where $a_{1} = 256$.

Therefore, the number of players compete in round 7 will be $a_{7} = 256 \times (\frac{1}{2} )^{(7 - 1)} = 4$. (Answer)