Exercise 12.2: Analyze the pattern of blocks in a sequence of buildings. Draw the next building, count blocks in level 1, and derive a rule.

The sequence shows buildings with 1, 2, and 3 levels. The next building will have 4 levels.
It will be structured as:

• 1 block at the top (Level 4)
• 2 blocks below that (Level 3)
• 3 blocks below that (Level 2)
• 4 blocks at the bottom (Level 1)

Based on the color pattern (Blue for topmost, Red for second from top, Green for third from top, then cycling), the colors for Building 4 would be:

• Topmost (1 block): Blue
• Second from top (2 blocks): Red
• Third from top (3 blocks): Green
• Bottommost (4 blocks): Blue

For a building with 'n' levels, the number of blocks in its bottommost row (labeled "level 1" in the diagram) is 'n'.

The rule is: The number of blocks in level 1 is equal to the building number (which is also the number of levels).
Expressed as a formula:

• For Building 3: Building number is 3. According to the rule, Blocks in Level 1 = 3. From the image, Building 3 has 3 blocks in its bottommost row (Level 1). So, $3 = 3$. The rule is correct.

• For Building 4: Building number is 4. According to the rule, Blocks in Level 1 = 4. From the pattern, Building 4 would have 4 blocks in its bottommost row (Level 1). So, $4 = 4$. The rule is correct.

Using the rule from Step 3:

If a building has 37 blocks in Level 1, then:

Therefore, the building will have 37 levels.