1/2 7/8 5/4 13/8 find the next number in the pattern

To find the next number in the sequence \( \frac{1}{2}, \frac{7}{8}, \frac{5}{4}, \frac{13}{8} \), let’s analyze how each term relates to the previous one.

1. **Convert to decimal form** (to identify any potential pattern more easily):
   - \( \frac{1}{2} = 0.5 \)
   - \( \frac{7}{8} = 0.875 \)
   - \( \frac{5}{4} = 1.25 \)
   - \( \frac{13}{8} = 1.625 \)

2. **Calculate the differences** between consecutive terms:
   - \( 0.875 - 0.5 = 0.375 \)
   - \( 1.25 - 0.875 = 0.375 \)
   - \( 1.625 - 1.25 = 0.375 \)

Each term increases by \( 0.375 \), suggesting an **arithmetic sequence** with a common difference of \( 0.375 \).

3. **Find the next term** by adding \( 0.375 \) to \( 1.625 \):
   \[
   1.625 + 0.375 = 2.0
   \]

In fractional form, \( 2.0 \) is \( \frac{2}{1} \).

### Answer:
The next number in the pattern is \( \frac{2}{1} \) or simply \( 2 \).

Would you like further details or have any questions?

#### Related Questions:
1. What is an arithmetic sequence, and how is it identified?
2. How can you convert fractions to decimal form accurately?
3. What other types of sequences exist besides arithmetic?
4. How do you identify a geometric sequence?
5. How can sequences be applied in real-world scenarios?

#### Tip:
When analyzing sequences, checking the differences between terms can often reveal the underlying pattern easily.

Discover how to determine the next number in the sequence 1/2, 7/8, 5/4, 13/8 by identifying the pattern and using an arithmetic sequence. Learn key concepts such as fractions to decimals conversion and arithmetic sequence rules, suitable for Grades 6-8.

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