The given sequence is:

$25, 30, 35, \dots$

Step 1: Analyze the Sequence

This sequence is an arithmetic sequence because the difference between consecutive terms is constant.

• First term ($a_1$): $25$
• Common difference ($d$): $30 - 25 = 5$

Step 2: Write the Explicit Formula

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

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

Substituting $a_1 = 25$ and $d = 5$:

$a_n = 25 + (n-1) \cdot 5$

Simplify the formula:

$a_n = 25 + 5n - 5$ $a_n = 5n + 20$

Final Answer:

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

$a_n = 5n + 20$

Would you like me to demonstrate this formula with specific terms, or do you have any additional questions?

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5 Related Questions:

1. How do you derive the general formula for an arithmetic sequence?
2. What is the 10th term of the sequence using the explicit formula?
3. Can you explain the difference between explicit and recursive formulas?
4. How do you find the sum of the first $n$ terms in an arithmetic sequence?
5. What are some applications of arithmetic sequences in real-world scenarios?

Tip:

When working with sequences, always verify the common difference (for arithmetic) or ratio (for geometric) to ensure the formula fits.