https://file.aiquickdraw.com/mathbot/file/17299208788872gwa2qg7.jpg

Let's analyze each part:

### Part (a): Predicting the Next Numbers in the Sequence
The sequence is:
\[
2, 7, -3, 2, -8, -3, -13, -8, -18, \ldots
\]

Let's examine the differences between terms to see if there's a pattern:

1. \( 7 - 2 = +5 \)
2. \( -3 - 7 = -10 \)
3. \( 2 - (-3) = +5 \)
4. \( -8 - 2 = -10 \)
5. \( -3 - (-8) = +5 \)
6. \( -13 - (-3) = -10 \)
7. \( -8 - (-13) = +5 \)
8. \( -18 - (-8) = -10 \)

The differences alternate between \( +5 \) and \( -10 \). Following this pattern, the next two terms should be:
1. \( -18 + 5 = -13 \)
2. \( -13 - 10 = -23 \)

So, the next two terms are **-13** and **-23**.

### Part (b): Predicting the Next Symbol
The pattern of symbols shown is:
\[
M, \heartsuit, 8, M, 4, \heartsuit, \ldots
\]

Observing the repetition, it seems like the symbols alternate between three main symbols in the order \( M, \heartsuit, 8 \), followed by \( M, 4, \heartsuit \). This suggests a repeating cycle of six symbols.

Following this cycle, the next two symbols after \( M, \heartsuit, 8, M, 4, \heartsuit \) would be:
1. **8**
2. **M**

### Summary
The answers are:
- **(a)**: -13, -23
- **(b)**: 8, M

Would you like more details or have any questions?

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Here are five related questions to deepen understanding:
1. What is the difference between inductive and deductive reasoning?
2. Can you find another sequence that alternates patterns?
3. How would you identify a repeating pattern in a more complex sequence?
4. What are common types of patterns found in symbol sequences?
5. Why might alternating differences be useful in real-world applications?

**Tip:** When identifying patterns, look for changes between terms first.

Use inductive reasoning to predict the next pattern.
a. 2, 7, -3, 2, -8, -3, -13, -8, -18, ___, ___
b. M, ♥, 8, M, 4, ♥, ___, ___

Explore the use of inductive reasoning to predict the next terms in a sequence. Learn how to analyze patterns with alternating differences and repeating symbols, suitable for Grade 8 students.

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