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- anonymous

John wants to determine the number of dots in step 20 without actually drawing them.
REST OF THE QUESTION IS IN THE PICTURE.

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- anonymous

- schrodinger

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- anonymous

- mathstudent55

Step 1 has 3 * 3 number of dots.
Step 2 has 4 * 4 number of dots.
Step 3 has 5 * 5 number of dots.
Ok?

- anonymous

yea would it be 20*20=400+@2? @mathstudent55

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- anonymous

also what is an algebraic expression i could put down? @mathstudent55

- mathstudent55

Be careful. We are asked about Step 20, right?

- anonymous

yea

- mathstudent55

Notice that Step 1 was not 1 * 1.
Step 2 was also not 2 * 2 dots.
Step 1 is 3 * 3. Step 2 is 4 * 4.
The pattern is that the numbers of dots you multiply together in each step are 2 more than the step you are in.
That means that for Step 20, you don't have 20 * 20 dots.
You have 22 * 22 dots.
Do you understand?

- mathstudent55

a. John notices that the numbers of dots multiplied in each step are 2 more than the step number, so he multiplies 22 * 22 to find the number of dots in step 20.

- mathstudent55

b. 22 * 22 = ?

- anonymous

one sec

- mathstudent55

ok

- anonymous

484

- anonymous

what would i put for a expression?

- mathstudent55

OK.
Let the step number be represented by n.
In step n, the numbers of dots you multiply together are 2 more than the step number, so the number of dots is 2 more than n. How do you represent 2 more than n in math?

- anonymous

+2?

- mathstudent55

Yes, but not just + 2.
It's
n + 2

- mathstudent55

Ok?
At step n, you need to multiply n + 2 by n + 2 to find the number of dots.
That means the formula is for step n is:
(n + 2)(n + 2)
We can write it more simply as
\((n + 2)^2\)

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