For each sequence in Table 3, describe the pattern, state whether the next shape can be drawn and why, and provide the rule or pattern for the sequence.

Here are the patterns and rules for each sequence in Table 3:

Sequence 1:

• Pattern: The sequence consists of squares made of smaller unit squares. The side length of the square increases by one unit in each step.
• Can you draw the next shape? Why or why not? Yes, the next shape can be drawn. The pattern is consistent: the side length of the square increases by 1 unit for each subsequent shape. The next shape would be a $4 \times 4$ square.
• Rule or pattern: The $n$-th shape in the sequence is an $n \times n$ square. The number of unit squares in each shape is the square of its position in the sequence, given by $n^2$.

Sequence 2:

• Pattern: The sequence consists of a single triangle, and its orientation alternates.
• Can you draw the next shape? Why or why not? Yes, the next shape can be drawn. The pattern is a clear alternation of the triangle's orientation. The next shape would be a single triangle pointing upwards.
• Rule or pattern: The shape is always a single triangle. Its orientation alternates between pointing upwards and pointing downwards.

Sequence 3:

• Pattern: The sequence consists of a horizontal row of circles. The number of circles in the row increases by one in each step.
• Can you draw the next shape? Why or why not? Yes, the next shape can be drawn. The pattern is consistent: one additional circle is added to the row for each subsequent shape. The next shape would be a row of 5 circles.
• Rule or pattern: The $n$-th shape in the sequence is a row of $n$ circles. The number of circles in the row is equal to its position in the sequence.