The problem mentions that the hourly salary follows an arithmetic sequence. We are given the hourly salaries for the first and second years:

• First year salary ($a_1$) = $8.50
• Second year salary ($a_2$) = $8.85

Step 1: Identify the common difference

In an arithmetic sequence, the common difference ($d$) is the difference between consecutive terms. Therefore, we can calculate the common difference as follows: $d = a_2 - a_1 = 8.85 - 8.50 = 0.35$

Step 2: Write the explicit rule for the nth term

The explicit formula for the nth term of an arithmetic sequence is given by: $a_n = a_1 + (n - 1) \cdot d$ Substitute $a_1 = 8.50$ and $d = 0.35$ into this formula: $a_n = 8.50 + (n - 1) \cdot 0.35$ Simplifying the expression: $a_n = 8.50 + 0.35n - 0.35$ $a_n = 8.15 + 0.35n$

Thus, the explicit rule for the hourly salary is: $a_n = 8.15 + 0.35n$

Let me know if you'd like any further clarifications or if you have any questions!

Related Questions:

1. How would you modify this formula if the salary increased by a different amount each year?
2. What would the salary be in the 5th year using this formula?
3. What is the general form of an arithmetic sequence?
4. Can an arithmetic sequence ever have a negative common difference? What would that represent in this context?
5. How do you find the sum of the first $n$ terms in an arithmetic sequence?

Tip:

When dealing with arithmetic sequences, remember that the difference between consecutive terms remains constant, which makes it easy to predict future terms.