Explain the pattern!

[kmarimon1]

I've tried to wrap my head around this. I've never really been good with this. Can someone solve/explain this?

This is how much a person made in each of the last four weeks working.

Week	Amount ($)
1	2
2	3
3	5
4	9

a) How much can the person expect to earn in the fifth week if this pattern continues?
b) Explain the pattern.

Thanks!
- Bobby Boucher

 

[Johnny_L]

I've tried to wrap my head around this. I've never really been good with this. Can someone solve/explain this?

This is how much a person made in each of the last four weeks working.

Week	Amount ($)
1	2
2	3
3	5
4	9

a) How much can the person expect to earn in the fifth week if this pattern continues?
b) Explain the pattern.

Thanks!
- Bobby Boucher

Each increment for the amount is doubling. I had trouble with it too, I think it would've helped if it had like 1 more example before it asked your, or if the difference's were more extreme

Week 5 is 17

 

[Ishuda]

Well obviously the formula for the series is A(1)=2, A(2)=3,
A(i)=3*A(i-1)-2*A(i-2)+1308.29167*(i-1)*(i-2)*(i-3)*(i-4) for i>2
Thus A(5)=31416

 

[Steven G]

Each increment for the amount is doubling. I had trouble with it too, I think it would've helped if it had like 1 more example before it asked your, or if the difference's were more extreme

Week 5 is 17

I agree that your answer is reasonable. You can always come up with other patterns that have your numbers as well. For example y=1 +(4/3)x -(1/2)x^2 +(1/6)x^3 will satisfy your 4 points yet y(5)=16, not 17.

 

[Ishuda]

And a "Huh?" to you too, Ishuda:shock:

I was tired of cake so I thought I would have something close to pi.

 

[soroban]

Hello, kmarimon1!

This is how much a person made in each of the last four weeks working.

. . \(\displaystyle \begin{array}{|c|c|}\hline\text{Week}&\text{Amount} \\ \hline
1 & 2 \\ \hline 2 & 3 \\ \hline 3 & 5 \\ \hline 4 & 9 \\ \hline \end{array}\)

How much can the person expect to earn in the fifth week
if this pattern continues?

Consider the differences of consecutive terms.

. . \(\displaystyle \begin{array}{c|ccccccc} \hline \text{Week} & 1 && 2 && 3 && 4 \\ \hline
\text{Amount} & 2 && 3 && 5&& 9 \\ \hline
\text{Difference}&& 1 && 2 && 4 \\ \hline \end{array}\)

The differences seem to be consecutive powers-of-2: \(\displaystyle 1,2,4,8,16 \text{ . . .}\)

If this is true, the fifth term is: .\(\displaystyle 9+8 \,=\,17\)

The general term is:. \(\displaystyle A(n)\:=\:1 +2^{n-1}\)