Let's analyze the sequence given: 1, 2, 3, 5, 5, 8, 7, 2, ?

1. Break the sequence into two parts for clarity:
   • First: 1, 3, 5, 7, ? (Odd positions)
   • Second: 2, 5, 8, 2 (Even positions)

First part (odd positions):

• The odd positions are: 1, 3, 5, 7, ?
• We notice a consistent increase of 2:
  • $1 \rightarrow 3$ (Increase by 2)
  • $3 \rightarrow 5$ (Increase by 2)
  • $5 \rightarrow 7$ (Increase by 2)

Therefore, the next number should be 7 + 2 = 9.

Second part (even positions):

• The even positions are: 2, 5, 8, 2
• There's a pattern where the numbers alternate:
  • $2 \rightarrow 5$ (Increase by 3)
  • $5 \rightarrow 8$ (Increase by 3)
  • $8 \rightarrow 2$ (Decrease by 6)

The next logical step would be an increase by 3 again, so 2 + 3 = 5.

Final sequence:

So, the next term in the sequence should be 9 in the odd positions and 5 in the even positions.

Answer:

Thus, the answer is C. 9, 10 (since the closest choice to 5 for even part is 10).

Would you like more details or have any questions?

Here are 5 relative questions that expand this information:

1. Can you create a similar sequence with a different pattern?
2. What happens if we change the increment pattern by a different number?
3. How would the solution change if the sequence alternated between addition and subtraction?
4. Can you predict the next two terms instead of just one?
5. How would you solve if no clear pattern appeared in the sequence?

Tip: When dealing with number sequences, try separating terms into different patterns (e.g., odd and even positions) for easier recognition.