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anonymous
 one year ago
John wants to determine the number of dots in step 20 without actually drawing them.
REST OF THE QUESTION IS IN THE PICTURE.
anonymous
 one year ago
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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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Step 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
 one year ago
Best ResponseYou've already chosen the best response.0yea would it be 20*20=400+@2? @mathstudent55

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0also what is an algebraic expression i could put down? @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Be careful. We are asked about Step 20, right?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Notice 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
 one year ago
Best ResponseYou've already chosen the best response.0a. 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what would i put for a expression?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0OK. 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?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Yes, but not just + 2. It's n + 2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Ok? 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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