Question

Timothy‘s salary, S(n), is a function of the number of years, n, that he has worked at his video game company. The relationship between n and S(n) is shown in the table below. Write an explicit geometric sequence that represents the information given in the table

Answer 1

On a geometric sequence, consecutive terms have a common ratio.

The formula for the n-th term a geometric sequence with first term a_1 an common ratio r is:

`S(n)=a_1\cdot r^(n-1)`

In this case, we can see that the first term is 30,000. To find the common ratio, divide the value of the second term by the value of the first term:

`\begin{gathered} r=(a_2)/(a_1) \\ =(36,000)/(30,000) \\ =1.2 \end{gathered}`

Substitute a_1=30,000 and r=1.2 to find the explicit formula for the geometric sequence:

`S(n)=30,000*1.2^(n-1)`