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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 =

Step 1 Step 2 Step 3 Using the figures above, how many small squares will there be-example-1
User Grexis
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1 Answer

14 votes
14 votes

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

User Dcmoody
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