Chapter 1.1, Problem 6MC

Mathematical Connections 1-2

The figure below shows the first three terms of a sequence of figures containing small square tiles. Some of the tiles are shaded. Notice that the first figure has one shaded tile. The second figure has $2\cdot 2$, or $2^2$, shaded tiles. The third figure has $3\cdot 3$, or $3^2$, shaded tiles. If this pattern of having shaded squares surrounded by white borders continues, answer the following:

a. How many shaded tiles are there in the $n^{th}$ figure?

b. How many white tiles are there in the $n^{th}$ figure?