Summing the functions of the previous function

[gallaga]

I have a base number that I would like to start with, with that number I would like to then add a mathematical function of itself to it and then repeat it a certain number of times. Therefore I would be taking the result of the base number + function and adding a function of the sum to the sum, resulting in another number

For example if I had a base number of 10 and an arbitrary denominator of 2:

I would take the base number, 10, then add (10 / 2) to it. From there I would like take that resulting number, which is (10 + (10/2)), and add ((10+(10/2)) / 2) to it.

We could replace (10 + (10/2)) with f(b), that is a function of the base number before it, and the equation would be f(b) = b + (b/2).

I want to come up with a one line formula for excel that takes the initial base number I give it and adds f(b) to f(b-1) a specified number of times (around 200 or so times).

Can anyone help?

 

[shg]

Welcome to the board.

In B1, enter 1

In A1, =IF(B1=1, 10, A1 + A1/2)

Enable the desired number of iterations (say, 20) and clear B1.

Or compute it in closed form: =10*(1 + 1/2)^20 ~ 33253

 

[gallaga]

Thanks for the help.

When I erase the 1 I get error 522 for a circular reference?

 

[shg]

You have to enable iteration. It Excel 2003, Tools > Options > Calculation ...

 

[gallaga]

I am now receiving error 523.

 

[shg]

Maybe skip the iteration and use the closed form solution; it's faster.