Putting Sequential numbers into a sloping line

[Jimmy]

I've been wracking my brain for the last 4 or 5 hours, trying to write myself a formula in excel. I stumbled across this site, and hope you can help me. I appologize if I'm in the wrong sub-forum, but it seemed appropriate.

I have a consecutive list of sequential numbers, 1 through 27 (all whole numbers, and all are present and accounted for). I need to write a formula so that I can plug in any number (X), and 1 = 8X, while 27 = 1X, with a perfectly sloping line in between.

i.e. If I plug in 50, then 1=400 and 27=50

I know this has got to be simple, and if I could remember far enough back to high school, or if I had paid attention in high school, I probably would have known what to do.

Thanks,
Jimmy

 

[stapel]

I'm sorry, but I don't understand what the actual question is...? What are you trying to do? What does the exercise instruct, exactly?

For instance, you say that you need a "formula" so that 1 = 8x (so x = 1/8) and 27 = 1x (so x = 27) for any value x. But that isn't possible! Your first equation fixed x as being 1/8 and your second assigned it the new value of 27. :shock:

Please reply with the exact text of the exercise. Thank you!

Eliz.

 

[Denis]

Looks like you're trying to make up an arithmetic series; that's a series where
each term is computed from the previous one by adding or subtracting a constant.

Let c = the constant; then your example would be:
[1]400, [2]400-c, [3]400-2c, .........., [26]400-25c, [27]400-26c = 50

c = (400 - 50) / 26 = 175/13

If you pick x=52 instead of 50, then 8x=416, so c = (416 - 52) / 26 = 14;
so this would give you an integer series:
[1]416, [2]402, [3]388, ....., [25]80, [26]66, [27]52

So in your case, c = (8x - x) / 26 = 7x / 26

If you need to do other cases (different from 27 terms),
then let n = number of terms, and formula becomes: c = 7x / (n-1)

You can also let m = multiples of x (8 in your example), and you'd get
this complete general case formula: c = x(m - 1) / (n-1),
and series would look like:
[1]mx, [2]mx-c, [3]mx-2c, .........., [n]mx-(n-1)c = x