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:

$\begin{gathered} r=\frac{a_2}{a_1} \\ =\frac{36,000}{30,000} \\ =1.2 \end{gathered}$

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

$S(n)=30,000\times1.2^{n-1}$