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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.

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  1. anonymous
    • one year ago
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  2. mathstudent55
    • one year ago
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    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?

  3. anonymous
    • one year ago
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    yea would it be 20*20=400+@2? @mathstudent55

  4. anonymous
    • one year ago
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    also what is an algebraic expression i could put down? @mathstudent55

  5. mathstudent55
    • one year ago
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    Be careful. We are asked about Step 20, right?

  6. anonymous
    • one year ago
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    yea

  7. mathstudent55
    • one year ago
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    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?

  8. mathstudent55
    • one year ago
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    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.

  9. mathstudent55
    • one year ago
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    b. 22 * 22 = ?

  10. anonymous
    • one year ago
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    one sec

  11. mathstudent55
    • one year ago
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    ok

  12. anonymous
    • one year ago
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    484

  13. anonymous
    • one year ago
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    what would i put for a expression?

  14. mathstudent55
    • one year ago
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    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?

  15. anonymous
    • one year ago
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    +2?

  16. mathstudent55
    • one year ago
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    Yes, but not just + 2. It's n + 2

  17. mathstudent55
    • one year ago
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    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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