The sequence shown in the image is:

$35, 32, 29, 26, 23, \ldots$

This is an arithmetic sequence, where each term decreases by 3. The formula for the $n$-th term of an arithmetic sequence is:

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

Where:

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

Step 1: Identify the first term and common difference

• First term, $a = 35$,
• Common difference, $d = -3$.

Step 2: Substitute into the formula

$t_n = 35 + (n - 1)(-3)$

Simplify:

$t_n = 35 - 3(n - 1)$

$t_n = 35 - 3n + 3$

$t_n = 38 - 3n$

Final Expression:

$t_n = 38 - 3n$

This is the expression for the $n$-th term of the sequence.

Would you like a further breakdown or have any questions?

Here are 5 related questions to explore:

1. How would the formula change if the common difference was positive?
2. Can you find the 10th term of this sequence using the formula?
3. What is the sum of the first 10 terms of this arithmetic sequence?
4. How can you determine if a sequence is arithmetic?
5. How would the formula be affected if the first term changed?

Tip: When writing arithmetic sequence formulas, always double-check the common difference and first term to avoid errors.