To solve the problem, let's start with the formula for the $n$-th term of an arithmetic sequence:

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

Where:

• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Step 1: Substitute values

Here, the common difference $d = -5$, and we want the 15th term ($n = 15$):

$a_{15} = a + (15-1)(-5)$

Step 2: Simplify the expression

$a_{15} = a + 14(-5)$ $a_{15} = a - 70$

Final Expression

The 15th term of the sequence is:

$a_{15} = a - 70$

Would you like a detailed explanation of arithmetic sequences? Let me know if you have any other questions!

Here are 5 related questions you can explore:

1. How do you derive the formula for the $n$-th term of an arithmetic sequence?
2. What happens if the common difference is positive? Can you solve a similar example?
3. How do you find the sum of the first $n$ terms of an arithmetic sequence?
4. If the first term $a = 10$, what is the 15th term in this sequence?
5. How would you find the term number $n$ for a specific value of $a_n$?

Tip: Always double-check the signs of the common difference $d$ when solving arithmetic sequence problems—it impacts the addition or subtraction in each term.