The given sequence is:

$7, 35, 175, \dots$

To identify the pattern, we can look at the ratio between consecutive terms:

$\frac{35}{7} = 5 \quad \text{and} \quad \frac{175}{35} = 5$

Since the ratio between consecutive terms is constant, this is a geometric sequence with a common ratio $r = 5$ and the first term $a_1 = 7$.

The general formula for the $n$-th term of a geometric sequence is:

$a_n = a_1 \cdot r^{n-1}$

Substitute $a_1 = 7$ and $r = 5$:

$a_n = 7 \cdot 5^{n-1}$

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

$a_n = 7 \cdot 5^{n-1}$

Would you like more details or have any questions?

Here are 5 questions that expand on this concept:

1. How do you derive the formula for the $n$-th term of a geometric sequence?
2. What is the 6th term in the sequence using the formula $a_n = 7 \cdot 5^{n-1}$?
3. What happens if the common ratio $r$ is less than 1 in a geometric sequence?
4. Can you determine the sum of the first 5 terms of the given sequence?
5. How does a geometric sequence differ from an arithmetic sequence?

Tip: In a geometric sequence, if the common ratio is greater than 1, the terms grow exponentially.