https://file.aiquickdraw.com/mathbot/file/1736004662269ljjcbs83.jpg

The sequence shown in the image is:

\[ 0, 1, 1, 2, 4, 7, 13, 24, 44, \_ \]

To solve for the next number in the sequence, let's analyze the pattern:

---

### Step 1: Find the relationship between terms.
- Look at the differences between consecutive terms:
  \[
  1 - 0 = 1, \quad 1 - 1 = 0, \quad 2 - 1 = 1, \quad 4 - 2 = 2, \quad 7 - 4 = 3, \quad 13 - 7 = 6, \quad 24 - 13 = 11, \quad 44 - 24 = 20
  \]
- Differences: \[ 1, 0, 1, 2, 3, 6, 11, 20 \]

---

### Step 2: Analyze the second differences.
- Look at the differences of the differences:
  \[
  0 - 1 = -1, \quad 1 - 0 = 1, \quad 2 - 1 = 1, \quad 3 - 2 = 1, \quad 6 - 3 = 3, \quad 11 - 6 = 5, \quad 20 - 11 = 9
  \]
- Second differences: \[ -1, 1, 1, 1, 3, 5, 9 \]

---

### Step 3: Predict the next term in the second differences.
- The second differences themselves are not constant, but they follow a noticeable pattern. Observe:
  \[
  1, 3, 5, 9 \quad \text{(increasing unevenly)}.
  \]
  The difference between these terms is:
  \[
  3 - 1 = 2, \quad 5 - 3 = 2, \quad 9 - 5 = 4
  \]
  Thus, the next difference is likely \( 4 + 2 = 6 \), so the next second difference should be \( 9 + 6 = 15 \).

---

### Step 4: Use this to find the next difference in the sequence.
- Add \( 15 \) to the last first difference:
  \[
  20 + 15 = 35
  \]

---

### Step 5: Calculate the next term in the original sequence.
- Add \( 35 \) to the last term (\( 44 \)):
  \[
  44 + 35 = 79
  \]

---

### Final Answer:
The next number in the sequence is:
\[
\boxed{79}
\]

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Would you like further clarification or a deeper exploration of this sequence?

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### 5 Related Questions:
1. How can you verify if a sequence follows a Fibonacci-like structure?
2. What are second differences, and how are they used in sequences?
3. Can you derive a formula for this specific sequence?
4. What other techniques are used to identify patterns in numerical sequences?
5. How are differences and sums used in solving real-world mathematical problems?

---

### Tip:
When solving number sequences, always start by looking at consecutive differences, as patterns often emerge from these calculations!

Discover how to analyze and solve numerical sequences with pattern recognition techniques. This example solves the sequence 0, 1, 1, 2, 4, 7, 13, 24, 44, ... and predicts the next term using differences and recursive patterns. Perfect for Grades 7-9.

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