The figures consist of three parts, each growing at their own unique rate.
a_x=x^2+4+3
Practice makes perfect
To determine a rule that represents the number of tiles in Figure x, we will divide it into three parts.
The tiles in the upper left part of the figure do not increase from one figure to the next. The tiles in the lower right part, however, increase by 1 from one figure to the next. To determine how the middle tiles grow we will rewrite the dimensions of the rectangles so that it includes the figure number.
With this information we can write a rule for the number of tiles in Figure x.
a_x= (x+2)(x+1)+ x+ 1
Let's rewrite this to a simpler form.
