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

Answer:

They earn $256 on the ninth day of school.

Step-by-step explanation:

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

$a_{n+1} = r \times a_{n}$

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:

$a_{n} = a_{1} \times r^{n}$

In which

$r = \frac{a_{n+1}}{a_{n}}$

In this question:

On the first day, $0.50. So $a_{1} = 0.5$.

Day two $1.00, day three $2.00.

So

$r = \frac{1}{0.5} = \frac{2}{1} = 2$

Then

$a_{n} = 0.5 \times 2^{n}$

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

$a_{9} = 0.5 \times 2^{9} = 256$

They earn $256 on the ninth day of school.