Question

Here is a pattern of squares.a. Sketch or describe the figure in Step 4 and Step 15.b. How many small squares will there be in each of these steps?c. Write an equation to represent the relationship between the step number, , and the number of small squares, , in each step.

Answer 1

For solving the problem we have to notice the following:

With this information we can predict the form of the figures n=4 and n=15

For each step, there will be

$n^2^{}$

small squares, where n is number of the step. So for step 4 there are 16 small squares and for n=15 there will be 225 small squares.

Finally the equation that represents the relation between the number of step and the number of small squares is

$\#\text{smallsquares}=(\#step)^2$