This sequence is: 3, 10, 29, 84, ?.

To identify the pattern, let's examine how the terms are generated.

1. First, observe the difference between consecutive terms:
   - \( 10 - 3 = 7 \)
   - \( 29 - 10 = 19 \)
   - \( 84 - 29 = 55 \)

2. Now, look at the differences between the differences:
   - \( 19 - 7 = 12 \)
   - \( 55 - 19 = 36 \)

3. These second differences (12, 36) show a multiplying pattern. Specifically:
   - \( 36 = 12 \times 3 \)

Following this pattern, the next difference between differences should be \( 36 \times 3 = 108 \).

4. Now add 108 to the last difference:
   - \( 55 + 108 = 163 \)

5. Finally, add this new difference to the last term of the sequence:
   - \( 84 + 163 = 247 \)

Thus, the next term in the sequence is **247**.

Would you like a deeper explanation of the pattern or further assistance?

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Here are five related questions:

1. What is the general formula for identifying a pattern in sequences?
2. How do you identify quadratic patterns in sequences?
3. Can you find the next term in the sequence 1, 4, 9, 16, 25, ...?
4. What is the difference between arithmetic and geometric sequences?
5. How can second differences help predict terms in a quadratic sequence?

**Tip:** When solving number sequences, always check the differences between terms first, as it often reveals the hidden pattern.

Discover how to find the next term in the sequence 3, 10, 29, 84, ? by analyzing second differences and recognizing quadratic patterns. This method is key for solving sequence problems in Grades 8-10.

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