anonymous
  • anonymous
John wants to determine the number of dots in step 20 without actually drawing them. REST OF THE QUESTION IS IN THE PICTURE.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
mathstudent55
  • 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
  • anonymous
yea would it be 20*20=400+@2? @mathstudent55

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anonymous
  • anonymous
also what is an algebraic expression i could put down? @mathstudent55
mathstudent55
  • mathstudent55
Be careful. We are asked about Step 20, right?
anonymous
  • anonymous
yea
mathstudent55
  • 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
  • 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
  • mathstudent55
b. 22 * 22 = ?
anonymous
  • anonymous
one sec
mathstudent55
  • mathstudent55
ok
anonymous
  • anonymous
484
anonymous
  • anonymous
what would i put for a expression?
mathstudent55
  • 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
  • anonymous
+2?
mathstudent55
  • mathstudent55
Yes, but not just + 2. It's n + 2
mathstudent55
  • 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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