The problem describes an arithmetic sequence where the man's salary increases by $750$ each year. The initial salary is $3,600$, and we need to find his salary during the 10th year.

Step 1: Identify the given values

• First term (initial salary), $a = 3600$
• Common difference (annual raise), $d = 750$
• We need to find the salary during the 10th year, i.e., the 10th term $a_{10}$.

Step 2: Use the formula for the $n$-th term of an arithmetic sequence

The $n$-th term of an arithmetic sequence is given by:

$a_n = a + (n-1) \cdot d$

Substitute the known values to find $a_{10}$:

$a_{10} = 3600 + (10-1) \cdot 750$

$a_{10} = 3600 + 9 \cdot 750$

$a_{10} = 3600 + 6750$

$a_{10} = 10350$

Final Answer:

The man's salary during the 10th year of his employment will be $10,350.

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Would you like more information on how to sum the salaries over multiple years or any other related queries?

Here are 5 related questions for practice:

1. What will the man's salary be in the 15th year of his employment?
2. How much total salary will he earn by the end of the 10th year?
3. What is the common difference in an arithmetic sequence, and how does it affect the sequence?
4. How does the salary progression change if the raise becomes $1,000 each year instead of $750?
5. If the initial salary were $4,000, what would the 10th-year salary be?

Tip: In arithmetic sequences, knowing the common difference and the first term lets you easily calculate any term using the formula for the $n$-th term.