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* 1= 4 square inches.
Let's now consider the second figure.
The second figure has 9 small squares. Therefore, its area is 9* 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* 1= 25 square inches. We can now write a sequence whose terms are the areas of these figures.
4, 9, 25
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 notconstant. In other words, there is not a common difference. Therefore, the sequence cannot be arithmetic.
