## Formula for Recurring Values

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

### Formula for Recurring Values

Hello all. I am a new poster in these forums, but have long followed posted topics. I am currently trying to figure out a method of determining an end value that can be duplicated given specific values. Of course, I am by no means a professional at writing word problems, so feel free to let me know if you think there would be any additional information/clarification that is needed.

Essentially, let's say that a series of sales data (by week) is given. Because this is quarterly data, each series consists of 12 weeks. Every fourth week, the data repeats.

Example:

Week 1: 10,000
Week 2: 9,000
Week 3: 9,500
Week 4: 11,000
Week 5: 10,000 (from week 1) + new sales (\$)
Week 6: 9,000 (from week 2) + new sales (\$)
Week 7: 9,500 (from week 3) + new sales (\$)
Week 8: 11,000 (from week 4) + new sales (\$)
.
.
.

If there is no new data after week 12, what would be the total annual sales?
derikg

Posts: 2
Joined: Mon Oct 21, 2013 7:36 pm

What do you mean by an "end value"? What do you mean by "duplication"? What do you mean by "repeated"? How do the "new sales" relate to the first four weeks of sales? How do the (unstated) values in weeks 9 through 12 relate to weeks 1 through 8? What assumptions are being made? What is meant by "no new data"? What is the "total" that you're looking for?

It might help if you provided the exact text of the exercise, along with its instructions. Thank you!

stapel_eliz

Posts: 1797
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Formula for Recurring Values

Thanks for the reply! To clarify, this is simply a personal endeavor that I've taken to developing formulas. Below is a link to the spreadsheet I've used as a way to check any formula written.

Beginning on the second page, you'll see weeks with corresponding numbers below. Each number highlighted in below is considered "new" sales. Looking further, you'll see each figure repeats every four weeks. This is done over and over until 48 weeks is reached. From there, you can see that the amount is totaled. That totaled amount is the end figure.

As a starting point, the formula I've put together is as follows:

= (Week1+Week2+Week3+Week4)*12+(Week5+Week6+Week7+Week8)*11+(Week9+Week10+Week11+Week12)*10

Of course, I assumed there is a simpler way to word this. I also cannot explain why the number being multiplied against (12,11,10) have to decrease. I know this is a complete cluster, but any help or direction you can give is greatly appreciated
derikg

Posts: 2
Joined: Mon Oct 21, 2013 7:36 pm

Sorry, but I'm not gonna open up a file. If you don't know why the formula has been set up the way it has, it's not really possible to figure out how to create a "correct" formula for whatever it is that you're doing. We really do need specific and complete information before advising how to proceed. Until we know what's going on, it's not possible to model it.

For instance, if the same exact sales amounts repeat every four weeks, and if you're trying to project the sales over fifty-two weeks, given the sales for the first four weeks, all you'd have to do is multiply the sum of the first four weeks by twelve (to get the sun for the first 12*4 = 48 weeks), and then add in another half-cycle. But apparently that's not what you're doing, so I have no idea where to go with it.

stapel_eliz

Posts: 1797
Joined: Mon Dec 08, 2008 4:22 pm