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!