To find the pattern in the sequence \( 7, 14, 8, 16, 10, 12, ? \), we can analyze the differences and possible relationships between consecutive terms.

1. **Identify the pattern:**
   - Consider separating the sequence into two interleaved subsequences:
     - Odd-positioned terms: \( 7, 8, 10, ? \)
     - Even-positioned terms: \( 14, 16, 12 \)

2. **Analyze the odd-positioned terms:** \( 7, 8, 10, ? \)
   - From 7 to 8, we add 1: \( 7 + 1 = 8 \)
   - From 8 to 10, we add 2: \( 8 + 2 = 10 \)
   - If the pattern continues by adding 1 more each time, the next number should be \( 10 + 3 = 13 \).

3. **Analyze the even-positioned terms:** \( 14, 16, 12 \)
   - From 14 to 16, we add 2: \( 14 + 2 = 16 \)
   - From 16 to 12, we subtract 4: \( 16 - 4 = 12 \)
   - This suggests a pattern alternating between adding and subtracting: \( +2, -4 \).
   - If we follow this alternating pattern, the next step would be to add 6 (to reverse the alternating change): \( 12 + 6 = 18 \). However, since we are focusing on filling the odd-position, this calculation is supplementary information.

4. **Identify the missing number:**
   - Based on the pattern identified for odd-positioned numbers, the missing number that completes the sequence is \( 13 \).

Thus, the missing number in the sequence is **13**.

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Would you like further details or have any questions? Here are a few related questions that can extend this topic:

1. How do you determine if a sequence has multiple valid patterns?
2. What are common types of numerical sequences and their general forms?
3. How can you identify the general term of a sequence?
4. What techniques can be used to solve more complex sequences with varying patterns?
5. How does recognizing arithmetic or geometric sequences help in solving problems?

**Tip:** Breaking down a sequence into separate patterns can often reveal hidden structures or rules, making complex problems more manageable.

Discover how to identify patterns in number sequences with a detailed analysis of the sequence 7, 14, 8, 16, 10, 12, ?. Learn about interleaved subsequences and alternating patterns in odd and even-positioned terms. Suitable for students in Grades 7-9.

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