Question

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Answer 1

Week 1: 300
Week 2: 450
Since this is a geometric sequence, what is the common ratio?

Answer 2

Im not sure.

Answer 3

It's easy. Divide a number by the number to its immediate left.

Answer 4

What is 450/300 ?

Answer 5

So the common thing that they multiply with is 1.5

Answer 6

So how would i get that up to week 20?

Answer 7

Notice that 450/300 = 1.5
Also, 675/450 = 1.5
Each next number is 1.5 times the previous number.
Ok so far?

Answer 8

okay I got it.

Answer 9

Now we will make our own formula for this pattern.

Answer 10

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.

Answer 11

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?

Answer 12

Did you get an answer?