The Growing Pyramid
Below is a sequence that examines the relationship between the figure number and the number of small shaded triangles in the figure.
1) Click in the "Graphics" side to open the Graphics Toolbar. Create Figure 4 using the “Wrench” feature in the toolbar. Choose “1 Group” in the drop-down. Once objects are created, you will need to go back to the "Pointer" tool to click and drag objects to where you want them. Write the figure number and number of triangles in the table. Click on each cell in the table to fill in the numbers. The ordered pair will automatically be created.
2) Create Figure 5 using the “Wrench” feature in the toolbar. Choose “3 Groups” in the drop-down. Write the figure number and number of triangles in the table.
3) Determine the function that represents the relationship between figure number and the number the triangles in the figure. Write it in the “Input” box at the bottom as “f(x) = ”.
4) If the pattern continues, how many triangles will be in the 7th figure?