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Draw the next building in the sequence and count the blocks in level 1 of each building.

Mathematics

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Answer

4\textbf{4}

1. Draw the next building in the sequence.

The pattern for the buildings is that each new building adds a new bottom layer with one more block than the previous building's bottom layer, and the existing layers are stacked on top.

  • Building 1 has 1 light blue block.
  • Building 2 has 2 red blocks at the bottom, with 1 light blue block on top.
  • Building 3 has 3 green blocks at the bottom, 2 red blocks in the middle, and 1 light blue block on top.

Following this pattern, Building 4 will have:

  • A bottom layer of 4 blocks (e.g., yellow blocks).
  • A layer of 3 green blocks on top of the middle two yellow blocks.
  • A layer of 2 red blocks on top of the middle green block.
  • A single light blue block on top of the middle red block.

Visually, it would look like this (imagine the colors as described):

□□□□□□□□□□\begin{array}{c} \square \\ \square \square \\ \square \square \square \\ \square \square \square \square \end{array}

(Where the top block is light blue, the next layer down is red, the next is green, and the bottom layer is a new color like yellow).

2. Count the blocks in level 1 of each building. In the table below, fill in the number of blocks in level 1 for buildings 1, 2, 3 and 4.

"Level 1" refers to the bottommost row of blocks in each building.

Building NumberNumber of blocks in Level 1
11
22
33
44

The completed table is:

Building NumberNumber of blocks in Level 111223344\begin{array}{|c|c|} \hline \text{Building Number} & \text{Number of blocks in Level 1} \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline 4 & \boxed{\textbf{4}} \\ \hline \end{array}
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