Answer:
[tex]a_{n} = a_{1} (\frac{1}{2} )^{n - 1}[/tex] where [tex]a_{1} = 256[/tex].
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 [tex]\frac{1}{2}[/tex] gives the number of players in the next round.
Therefore, the explicit function of number of players in nth round is given by
[tex]a_{n} = a_{1} (\frac{1}{2} )^{n - 1}[/tex] where [tex]a_{1} = 256[/tex].
Therefore, the number of players compete in round 7 will be [tex]a_{7} = 256 \times (\frac{1}{2} )^{(7 - 1)} = 4[/tex]. (Answer)
