https://file.aiquickdraw.com/mathbot/file/1729515189660ygll0cw6.jpg

The image presents a table showing a relationship between the **Pattern number** and the **Amount of blocks**. However, values for Pattern numbers 4 and 5 (labeled as **A** and **B**) are missing, and we need to determine these values.

The given data is:

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Pattern number} & 1 & 2 & 3 & 4 & 5 \\
\hline
\text{Amount of blocks} & 1 & 5 & 9 & A & B \\
\hline
\end{array}
\]

To find the missing values \(A\) and \(B\), we need to analyze the pattern in the **Amount of blocks**:

- For Pattern 1, the number of blocks is 1.
- For Pattern 2, the number of blocks is 5.
- For Pattern 3, the number of blocks is 9.

Let’s check if the differences between consecutive amounts are constant or follow a specific rule:

- Difference between Pattern 2 and Pattern 1: \( 5 - 1 = 4 \)
- Difference between Pattern 3 and Pattern 2: \( 9 - 5 = 4 \)

This suggests that the number of blocks increases by 4 for each subsequent pattern. If this trend continues, the number of blocks for Pattern 4 and Pattern 5 should be:

- \( A = 9 + 4 = 13 \)
- \( B = 13 + 4 = 17 \)

Thus, the completed table is:

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Pattern number} & 1 & 2 & 3 & 4 & 5 \\
\hline
\text{Amount of blocks} & 1 & 5 & 9 & 13 & 17 \\
\hline
\end{array}
\]

Would you like further clarification or a more detailed explanation on how I derived this pattern?

Here are 5 questions that extend this topic:
1. What would be the number of blocks for Pattern 6 based on this trend?
2. Can we express the number of blocks as a formula depending on the pattern number?
3. How would this sequence change if the increase between patterns wasn’t constant?
4. How do arithmetic sequences help in solving problems like this?
5. Could you find the sum of blocks up to Pattern 5?

**Tip:** Identifying constant differences between terms often points to an arithmetic sequence.

Find the missing values A and B for the pattern sequence where the amounts of blocks for Pattern 4 and 5 are missing.

Solve for the missing values A and B in a sequence of blocks based on an arithmetic pattern. The difference between terms is constant. This problem demonstrates how to analyze and extend an arithmetic sequence. Suitable for Grades 5-7.

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