Describe the pattern, rule, next shape, and reason for each of the three sequences in Table 3.

Here are the patterns 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.
• Rule: 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 ($n^2$).
• Next Shape: The next shape would be a $4 \times 4$ square, containing 16 unit squares.
• Why: Yes, the next shape can be drawn because the pattern is consistent: the side length of the square increases by 1 unit for each subsequent shape.

Sequence 2:

• Pattern: The sequence consists of a single triangle, and its orientation alternates.
• Rule: The shape is always a single triangle. Its orientation alternates between pointing upwards and pointing downwards.
• Next Shape: The next shape would be a single triangle pointing upwards.
• Why: Yes, the next shape can be drawn because the pattern is a clear alternation of the triangle's orientation.

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.
• Rule: 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.
• Next Shape: The next shape would be a row of 5 circles.
• Why: Yes, the next shape can be drawn because the pattern is consistent: one additional circle is added to the row for each subsequent shape.