excel - reverse of exponential sum

Question

HELP!!!

I'm trying to find a way, in Excel, to work out the base number from the sum of exponential values. However, it's not as straight forward as that because the first multiplier is different to the others

For example there might be:

First number : 10
10 * 3 = 30
30 * 1.5 = 45
45 * 1.5 = 67.5
67.5 * 1.5 = 101.25
when you add these together you get 253.75

(It won't always be the same multipliers or the same number of times it's multiplied)

Given that I know what the multipliers are (3 for first and 1.5 for the rest) I'm trying to work out a formula that will derive the first number (10) from the sum of the other values (253.75).

I hope that makes sense

I'd appreciate any help at all on this!

Answer 1

Your 3 (initial multiplier) is in the wrong place. Try this:

=253.75 * (1 - 1.5) / ((1 - 1.5) + 3 * (1 - 1.5^(5-1))

In the final (5-1), the 5 is the total number of steps backward from the total that one would find the original number.