Exercise 48 Page 206

We are told that the area of each small square represents $1$ square inch. Let's consider the first figure.

We see that the first figure contains four small squares. Therefore, its area is $4\times 1=4$ square inches. Let's now consider the second figure.

The second figure has $9$ small squares. Therefore, its area is $9\times 1=9$ square inches. Finally, let's consider the third diagram.

The third diagram has $25$ small squares. This means that its area is $25\times 1=25$ square inches. We can now write a sequence whose terms are the areas of these figures. The difference between the areas of the first and second figures is $9-4=5$ square inches. Conversely, the difference between the areas of the second and third figures is $25-9=16$ square inches. This means that the difference between consecutive terms is not constant. In other words, there is not a common difference. Therefore, the sequence cannot be arithmetic.