Question

What is the equation that represents the sequence in this problem ? Find the price after the 8th month

Answer 1

`\begin{gathered} a_n=ar^{n\text{ - 1}} \\ a_8\text{ = \$38.26} \end{gathered}`

Step-by-step explanation

The problem represents a geometric progression.

The general form of a geometric sequence is:

`a_n=ar^{n\text{ - 1}}`

where a = first term

r = common ratio

The first term from the table is the first price (for the first month). That is $80.00

To find the common ratio, we divide a term by its preceeding term.

Let us divide the price of the second month from the first.

We have:

`\begin{gathered} r\text{ = }(72)/(80) \\ r\text{ = 0.9} \end{gathered}`

The price after the 8th month is the value of a(n) when n = 8

So, we have that:

`\begin{gathered} a_8\text{ = 80 }\cdot0.9^{(8\text{ - 1)}} \\ a_8\text{ = 80 }\cdot0.9^7 \\ a_8\text{ = \$38.26} \end{gathered}`