Question

One the first day of school, each student is given $0.50 to attend. On day two, each student earns $1.00, day 3, $2.00, etc. How much do students earn on the ninth day of school?

Answer 1

They earn $256 on the ninth day of school.

Explanation:

A geometric sequence(in which each term is the previous term multiplied by the ratio) has the following format:

`a_(n+1) = r * a_(n)`

In which r is the common ratio.

We can also find the nth term as a function of the first term, by the following equation:

`a_(n) = a_(1) * r^(n)`

In which

`r = (a_(n+1))/(a_(n))`

In this question:

On the first day, $0.50. So
`a_(1) = 0.5`.

Day two $1.00, day three $2.00.

So

`r = (1)/(0.5) = (2)/(1) = 2`

Then

`a_(n) = 0.5 * 2^(n)`

How much do students earn on the ninth day of school?

`a_(9) = 0.5 * 2^(9) = 256`

They earn $256 on the ninth day of school.