The sequence you've provided is:

$28, 34, 40, \ldots$

This appears to be an arithmetic sequence, where the difference between consecutive terms is constant. To find the explicit formula for the $n$-th term, let's break it down:

Step 1: Identify the first term and common difference

• First term ($a_1$) = 28
• Common difference ($d$) = 34 - 28 = 6

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

The general formula for the $n$-th term of an arithmetic sequence is:

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

Where:

• $a_n$ is the $n$-th term,
• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Step 3: Substitute the values

Substitute $a_1 = 28$ and $d = 6$ into the formula:

$a_n = 28 + (n - 1) \cdot 6$

Simplifying:

$a_n = 28 + 6n - 6$ $a_n = 6n + 22$

Final Answer:

The explicit formula for the $n$-th term of the sequence is:

$a_n = 6n + 22$

Would you like further clarification or details on this? Here are some related questions to explore:

1. What is the 10th term of the sequence?
2. How do you derive the formula for the sum of the first $n$ terms of an arithmetic sequence?
3. What is the common difference in an arithmetic sequence, and how does it affect the sequence?
4. Can the common difference in an arithmetic sequence be negative? What happens then?
5. How can you identify if a sequence is arithmetic or geometric?

Tip: When working with arithmetic sequences, always check the difference between consecutive terms to ensure it's constant.