5, 11, 10, 4, 6, 12, 9 what is the next number

To find the next number in the sequence \( 5, 11, 10, 4, 6, 12, 9 \), let's analyze any patterns:

- Consider alternating differences:
  - From 5 to 11: +6
  - From 11 to 10: -1
  - From 10 to 4: -6
  - From 4 to 6: +2
  - From 6 to 12: +6
  - From 12 to 9: -3
  
A possible next difference could continue the alternating pattern of differences:
- The differences alternate between positive and negative values, and the positive ones are increasing by 2 each time. Following this, the next positive difference should be +8.
  
Therefore, the next number after 9 is:

\[
9 + 8 = 17
\]

So, the next number in the sequence is **17**.

Would you like more details or have any questions?

Here are some related questions for practice:
1. Can you determine the next number if the sequence followed a different alternating pattern?
2. What would the 10th number in the sequence be?
3. How would the pattern change if the increments decreased by 1 instead of increasing?
4. Can you identify a different mathematical rule to describe this sequence?
5. What happens if we apply a geometric progression instead of an arithmetic pattern?

**Tip:** When analyzing sequences, always check for alternating or repeating patterns in differences!

Discover how to find the next number in the sequence 5, 11, 10, 4, 6, 12, 9 by analyzing alternating differences and applying basic arithmetic patterns. This step-by-step guide explains the method used to arrive at the answer and is suitable for students in Grades 6-8.

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