Fitting a constant multiplier to a series to attain a specific sum at a specific length.

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sorry about the title. I am not a math guy and the following question is way beyond me.

The following is for utility in a TSP solving algorithm I am writing.

I have a list of coefficients that I use while the algorithm is running, but under certain conditions I need to alter the list. I need to alter it up to a specific point in the list, and the point is unknown until the condition is met.

So let's say I have a list, [.75, .75, .75, .75 ......], where each value is a coefficient for a certain iteration of my loop. And then on iteration... say... 35, my algorithm determined I need to alter the coefficients. I need to alter them up to the 35th entry in the list.

However, I want to alter them with the following conditions:

The 35th (or whatever the last entry was) needs to be bumped up by .1 Every other entry needs to be bumped up by some value, such that they form a series of [the fibonacci sequence] * C, where C is some constant that we can multiply every entry with such that the 35th(just in this example) number equals .1

So, yeah. I have no idea how to do this. It'd actually be nice to get some intuition on how to do this for any type of sequence, actually.

Thanks for any help.