This problem involves calculating the total earnings of a middle school mathematics teacher over a 40-year period. The teacher's salary starts at $30,000, and each year, the salary increases by $1,000.

This is a classic example of an arithmetic series. The formula for the sum of an arithmetic series is given by:

$S_n = \frac{n}{2} \times (2a + (n - 1) \cdot d)$

Where:

• $S_n$ is the total sum over $n$ years,
• $a$ is the initial salary (in this case, $30,000),
• $d$ is the annual raise (in this case, $1,000),
• $n$ is the number of years (in this case, 40).

Let me compute that for you.The total amount the middle school mathematics teacher will earn over the first 40 years is $1,980,000.

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How would the total earnings change if the raise were $500 instead of $1000?
2. What is the average yearly salary over the 40 years?
3. How much would the teacher earn after 20 years under the same conditions?
4. How does the formula change if the raise increases by a percentage rather than a fixed amount?
5. What would the total earnings be if the starting salary were $35,000?

Tip: When dealing with increasing payments or salaries, use arithmetic series to quickly sum them over a period.