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

`a_(n) = a_(1) ((1)/(2) )^(n - 1)` where
`a_(1) = 256`.

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

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
`(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) ((1)/(2) )^(n - 1)` where
`a_(1) = 256`.

Therefore, the number of players compete in round 7 will be
`a_(7) = 256 * ((1)/(2) )^((7 - 1))  = 4`. (Answer)