It looks like you're providing a sequence of numbers: 26, 11, 15, -4, 19, -23, 42, 65, and you're asking about the next number (or the general pattern).

To identify the pattern, let's look at the differences between consecutive numbers:

1. \( 11 - 26 = -15 \)
2. \( 15 - 11 = 4 \)
3. \( -4 - 15 = -19 \)
4. \( 19 - (-4) = 23 \)
5. \( -23 - 19 = -42 \)
6. \( 42 - (-23) = 65 \)
7. \( 65 - 42 = 23 \)

The sequence of differences is: \(-15, 4, -19, 23, -42, 65, 23\).

It appears the differences alternate between positive and negative values, but the pattern is not immediately obvious. Let me check further and calculate whether the next number follows a consistent rule. Based on the differences, I can continue the pattern.

The most likely next step is to subtract \( -42 \) from 65. That would give:

\[
65 + (-42) = 23
\]

Thus, the next number after 65 is **23**.

Would you like a more detailed breakdown of this sequence or how I derived this?

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### Follow-up questions:
1. Could this sequence involve any hidden mathematical formula?
2. Should we investigate a different approach, like geometric or recursive sequences?
3. Are you interested in how to predict future terms beyond the next?
4. Would you like help with sequences that follow a quadratic or higher-degree rule?
5. Do you need assistance understanding the logic behind alternating sequences?

**Tip:** In number sequences, always check both differences between terms and possible ratio patterns (geometric sequences) when identifying the next number.

Explore the number sequence 26, 11, 15, -4, 19, -23, 42, 65 and learn how to identify the next number by recognizing alternating difference patterns. This problem covers key mathematical concepts like arithmetic sequences and pattern recognition, suitable for students in Grades 8-10.

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