Quote (https://support.google.com/docs/answer/3093444)
Syntax
SERIESSUM(x, n, m, a)
x - The input to the power series. Varies depending on the type of approximation, may be angle, exponent, or some other value.
n - The initial power to which to raise x in the power series.
m - The additive increment by which to increase x.
a - The array or range containing the coefficients of the power series.
While I don't completely understand what you are trying to do, I might be able to help a little:
remember A4+a4*1.25+A4*1.25^2 = A4*1.25^0 + A4*1.25^1 + A4*1.25^2, this makes it more obvious what to do.
=SERIESSUM(1.25, 0, 1, {A4,A4,A4} )
notice that m needs to be 1, we want the power to increase by 1 each time
notice that n is 0, we started the power at 0
notice that a is an array of the coefficients, your example had the same coefficient each time (A4). You might also notice that the size of this array (the number of entries in the array) determines how many members of the series we will be summing (in this case 3).
The only problem I see is how to populate this array automatically, but since I don't really understand what you are trying to do, I'm not sure how to go about that.
Hopefully this nudges you in the right direction.