It looks like you have provided a sequence of numbers: \( \frac{1}{2}, 1, \frac{7}{4}, \frac{5}{2} \). Let’s analyze the sequence to identify its pattern.

We can first express all terms with the same denominator to better understand the differences between the terms:

- \( \frac{1}{2} = \frac{2}{4} \)
- \( 1 = \frac{4}{4} \)
- \( \frac{7}{4} \) stays as is.
- \( \frac{5}{2} = \frac{10}{4} \)

So the sequence becomes: \( \frac{2}{4}, \frac{4}{4}, \frac{7}{4}, \frac{10}{4} \).

Now, let’s find the differences between consecutive terms:
- \( \frac{4}{4} - \frac{2}{4} = \frac{2}{4} = \frac{1}{2} \)
- \( \frac{7}{4} - \frac{4}{4} = \frac{3}{4} \)
- \( \frac{10}{4} - \frac{7}{4} = \frac{3}{4} \)

We observe that after the first difference, the remaining differences are constant at \( \frac{3}{4} \). This suggests that after the first term, the sequence follows an arithmetic progression with a common difference of \( \frac{3}{4} \).

### Next Term in the Sequence
To find the next term:
\[
\frac{5}{2} + \frac{3}{4} = \frac{10}{4} + \frac{3}{4} = \frac{13}{4}
\]
So, the next term is \( \frac{13}{4} \).

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How do you find the common difference in an arithmetic sequence?
2. What is the general formula for the \(n\)-th term of an arithmetic sequence?
3. How can we determine if a sequence is arithmetic or geometric?
4. How do you find the sum of the first \(n\) terms in an arithmetic sequence?
5. Can an arithmetic sequence have negative terms or a decreasing pattern?

**Tip:** In arithmetic sequences, once you find a pattern in the differences between consecutive terms, you can predict future terms using the common difference.

Learn how to analyze an arithmetic sequence involving fractions, starting with 1/2, 1, 7/4, and 5/2. This step-by-step guide covers identifying the common difference and predicting future terms. Suitable for Grades 6-8 students learning about sequences and arithmetic progressions.

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