Question

Step 1 Step 2 Step 3 Using the figures above, how many small squares will there be in step 4 and step 15? a. Step 4 = b. Step 15 =

Answer 1

Step 4 = 16 squares

Step 15 = 225 squares

1) In the 1st step we can see, 1 square. In the 2nd, 4, and on the third one 9

So there's a sequence, 1, 4, 9

2) We can write the positions and raise them to the 2nd power we can see how it grows:

position (steps) n | 1 | 2 | 3

# squares | 1 | 4 | 9

3) We can derive a formula for that sequence:

$a_n=n^2$

Following this rule, we can find that

Step 4 = 4² = 16 squares

Step 15 = 15² = 225 squares