The problem asks for the formula of the $n$-th term of the sequence: $\frac{1}{2}, \frac{3}{5}, \frac{5}{8}, \frac{7}{11}, \dots$ We can analyze the numerators and denominators separately:

• Numerators: $1, 3, 5, 7, \dots$. This sequence increases by 2 each time. So, the formula for the $n$-th term of the numerator is: $\text{Numerator} = 2n - 1$

• Denominators: $2, 5, 8, 11, \dots$. This sequence increases by 3 each time. So, the formula for the $n$-th term of the denominator is: $\text{Denominator} = 3n - 1$

Thus, the general formula for the $n$-th term of the sequence is: $\frac{2n - 1}{3n - 1}$

Comparing this with the given options, the correct answer is: $\boxed{c. \frac{2n - 1}{3n - 1}}$

Would you like more details, or do you have any further questions?

Here are 5 related questions for practice:

1. What is the 5th term of this sequence?
2. How would you find the formula for a sequence with a different pattern in the numerators and denominators?
3. Can you derive a general approach for solving sequences with linear patterns?
4. What happens if the sequence includes non-linear terms?
5. How would you check if a sequence is arithmetic or geometric?

Tip: Always analyze the sequence's numerators and denominators separately for fractional sequences like this.