Formula to calculate deductions in 48-week period and yield a 52-week value

Hello,
I am in desperate need of assistance. I am at wits end and not sure if what I need done is even possible. What I am ultimately trying to achieve is to administer weekly deductions over a 48-week period that yield a 52-week value. I am currently using a spreadsheet to calculate deduction totals over a 48-week period based on a number entered into cell i8. The problem I am having, is when I try to add the sum result of weeks 49 through 52 to the calculated table which, at this point of the process has to be divided by 48 weeks and then added to the first calculated result of the first 48 weeks. However, weeks 49 through 52 would have to be excluded because this total value would now have been spread across the 48-week period. The idea is to first calculate the total amount of deductions over the 52-week period based on the contents of the value of cell $i$8. Next, I need to add the sum of weeks 49-52 and divide the sum by the 48-week deduction period, and finally add those results to the 48 weeks. So far everything I have tried gives me an error.

The first calculating cell on the sheet is cell C11 containing the following =B11*$I$8 with the value of I8 being 4 so the immediate results of cell C11 shows 4. When I copy this formula down through the subsequent cells the results increase by 4 with C12 = to 8, C13 = to 12, and so on. What I would like the formula to do is use the result of I32 (which represents the total for week 48) and simulate the increment totals for the remaining weeks. If we use the example of 4 the sum total would be 808/48 yielding a result of 16.83 to be added to the 48-week totals with a new result in cell C11 now being 20.83. To make things more complex we have to remember that the current value of $I$8 being (4) for all intents and purposes is arbitrary, and could be any number or value when using this sheet to calculate totals. I am hopeful that someone here can help. Thanks in advance.

I dunno what you're trying to do, but I'm pretty sure your math isn't doing that.

where in tarnation is that 808 in "sum total would be 808/48" come from?

The sum total is 4704, the mean is 4704/48 = 98.

You especially lost me with "new result in cell C11 now being 20.83" because isn't that just going to cause endless recursion, thus the answer is infinity?

I am well and truly flummoxed.

Ok, that's the simpler one.

What about the infinity thing?

Let's take a step back.

What exactly are you trying to do here? Where's this crazy arithmetic expansion of the deduction coming from, anyway?

The formula for the running total of your series for a given week is

=$I$8*B11*(B11+1)/2

where B11 is the week number. So you want to reverse engineer a value for that will give the same answer in week 48 that I8 gives for week 52. Is that right?

So the value for week 52 is

=$I$8*52*(52+1)/2

so a little algebra tells us that the adjusted value to replace I8 is

=($I$8*52*(52+1))/(48*(48+1))

So use this formula in C11 and copy down:

=B11*($I$8*52*(52+1))/(48*(48+1))

See attached.