Question

the graph shows ms. franklins salary for the first few years she worked at a company.

what is the explicit formula of the arithmetic sequence shown in the graph?
\\(a_n =\\)

if the pattern continues, what will ms. franklins salary be in year 10?

Explanation:

Identify the sequence terms

Using the Arithmetic Sequences knowledge point

$$
LATEXBLOCK0
$$

Find the common difference

Using the Arithmetic Sequences knowledge point

$$ d = a_2 - a_1 = 28800 - 28000 = 800 $$

Determine the explicit formula

Using the Arithmetic Sequence Explicit Formula knowledge point

$$
LATEXBLOCK1
$$

Calculate the salary in year 10

Using the Arithmetic Sequence Explicit Formula knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question 1

The explicit formula of the arithmetic sequence is:
\(a_n = 28000 + 800(n - 1)\) (or in simplified form, \(a_n = 27200 + 800n\))

Question 2

If the pattern continues, Ms. Franklin's salary in year 10 will be:
\(35200\) dollars