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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.

What is the formula for the n-th term of the sequence: 1/2, 3/5, 5/8, 7/11, ...?

Learn how to find the formula for the n-th term of the sequence: 1/2, 3/5, 5/8, 7/11. This math problem involves analyzing patterns in both numerators and denominators. The solution uses arithmetic sequence formulas to find the general expression for any n-th term. Suitable for students in Grades 9-12.

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