Explorations with patterns

1. For each of the following sequences of figures:

• draw the next figure,
• find the number of squares/triangles in each figure,
• find the number of squares/triangles in the 50th figure in the sequence,
• find the area and the perimeter of each of the first five figures and of the 50th figure in the sequence,
• organize your data in a table as shown in (a).

(a)

(b)

(c)

2. Create your own sequence of figures (using rectangles, triangles, hexagons, or any other shapes you like). Find the number(s) of shapes needed for the 50th figure in your sequence. Can you also find its area and/or perimeter?