Question

In a talent competition, half of the contestants are eliminated in each round. At the end of the nth round, 32 contestants remain. If there were 1,024 contestants at the start of the competition, what is the value of n?

Answer 1

n= 5, If half of the contestants were eliminated every round, the count would go like, 1024/2, 512/2, 256/2, 128/2, 64/2, 32.

Answer 2

Value of n = 6

Explanation:

This is an example of Geometric progression.

First term, a = 1024

Half of the contestants are eliminated in each round.

Common ratio, r = 0.5

We have n th term of GP

`a_n=ar^(n-1)`

Substituting

`a_n=ar^(n-1)=1024* 0.5^(n-1)`

At the end of the nth round, 32 contestants remain.

That is

`a_n=1024* 0.5^(n-1)=32\\\\0.5^(n-1)=0.03125=0.5^5\\\\n-1=5\\\\n=6`

Value of n = 6