Question

Write the first five terms of the sequence that represent the number of games in each round of the tournament. Let n = 1 be the first round of the tournament. Show the steps that you used to calculate the values in the sequence.

Answer 1

Answer: The first 5 times are 256 , 128 , 64 , 32 and 16

Explanation:

The situation is a scenario of Geometric sequence. The nth term for a geometric sequence is given as:

`t_(n)` = a
`r^(n-1)`

a = 256

r =1/2

substituting into the formula

when n = 1

`t_(1)` = 256(
`(1/2)^(1-1)`)

`t_(1)` = 256

when n = 2 ,this is the second round , we have

`t_(2)` = 256 x
`(1)/(2) ^(2-1)`

`t_(2)` = 128

When n = 3 , we have

`t_(3)` = 256 x 1/4

`t_(3)` = 64

when n = 4

`t_(4)` = 256 x 1/8

`t_(4)` = 32

when n = 5

`t_(5)` = 256 x 1/16

`t_(5)` = 16

Therefore the first five terms of the sequence that represent the number of games in each round of the tournament are:

256 , 128 , 64 , 32 , 16