From the image description, it appears that the number of squares in each step forms a perfect square. In step 1, there are 2 squares (which is $$1^2 + 1$$), in step 2, there are 4 squares (which is $$2^2$$), and in step 3, there are 9 squares (which is $$3^2$$).
So, the relationship between the step number (let's call it $$n$$) and the number of squares (let's call it $$S$$) can be represented by the equation:
$$S = n^2$$
In this equation:
- $$n$$ represents the step number. It's the input to our function.
- $$n^2$$ represents the number of squares in each step. It's the output of our function.
- The exponent of 2 indicates that the number of squares increases quadratically with each step.
This equation tells us that for any given step number $$n$$, the number of squares $$S$$ will be the square of that step number. For example, in step 4, there would be $$4^2 = 16$$ squares. This pattern continues for all subsequent steps. I hope this helps! Let me know if you have any other questions.