The image asks:

"What is the n-th term of an arithmetic sequence whose common difference is -2 and with first term 7?"

To solve this, use the formula for the n-th term of an arithmetic sequence:

$a_n = a_1 + (n-1) \cdot d$

Where:

• $a_n$ is the n-th term,
• $a_1$ is the first term (7 in this case),
• $d$ is the common difference (-2 in this case),
• $n$ is the term number.

Substituting the given values:

$a_n = 7 + (n-1) \cdot (-2)$

Simplifying:

$a_n = 7 - 2(n - 1)$ $a_n = 7 - 2n + 2$ $a_n = 9 - 2n$

Thus, the n-th term of the arithmetic sequence is:

$a_n = 9 - 2n$

Let me know if you want more details or have any questions!

Here are 5 related questions for deeper understanding:

1. How would the formula change if the common difference were positive?
2. What is the 10th term of this sequence?
3. How can you find the sum of the first $n$ terms of this sequence?
4. What is the first negative term in this arithmetic sequence?
5. How do you identify if a sequence is arithmetic based on its terms?

Tip: In an arithmetic sequence, the difference between consecutive terms remains constant, making it easy to calculate any term.