emmynimmy
  • emmynimmy
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Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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emmynimmy
  • emmynimmy
mathstudent55
  • mathstudent55
Week 1: 300 Week 2: 450 Since this is a geometric sequence, what is the common ratio?
emmynimmy
  • emmynimmy
Im not sure.

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mathstudent55
  • mathstudent55
It's easy. Divide a number by the number to its immediate left.
mathstudent55
  • mathstudent55
What is 450/300 ?
anonymous
  • anonymous
So the common thing that they multiply with is 1.5
emmynimmy
  • emmynimmy
So how would i get that up to week 20?
mathstudent55
  • mathstudent55
Notice that 450/300 = 1.5 Also, 675/450 = 1.5 Each next number is 1.5 times the previous number. Ok so far?
emmynimmy
  • emmynimmy
okay I got it.
mathstudent55
  • mathstudent55
Now we will make our own formula for this pattern.
mathstudent55
  • mathstudent55
Week 1: 300 Week 2: 300 * 1.5 Week 3: 300 * 1.5 * 1.5 Week 4 = 300 * 1.5 * 1.5 * 1.5 We begin to see a pattern. Week 1: 300 = 300 * 1.5^0 Week 2: 300 * 1.5 = 300 * 1.5^1 Week 3: 300 * 1.5 * 1.5 = 300 * 1.5^2 Week 4 = 300 * 1.5 * 1.5 * 1.5 = 300 * 1.5^3 For each week, multiply 300 by 1.5 raised to the power that is the week number minus 1.
mathstudent55
  • mathstudent55
Since Week 4 is \(300 \times 1.5^3\) Week 5 would be \(300 \times 1.5^4\) Then Week 20 is \(300 \times 1.5^?\) What does the ? stand for?
mathstudent55
  • mathstudent55
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