Originally Posted by

**sapph** I'm sure there's an easy way to do this, but its been ages since I did algebra.

I've got an arithmetic series. Each term increases by 10% of the original term. For instance: 40, 44, 48, 52, 56, etc.

The formula I've come up with to calculate the nth term is:

$\displaystyle v_{n}=v_{i}+(.1v_{i}(n-1))$

Where $\displaystyle v_{n}$ is the nth value and $\displaystyle v_{i}$ is the initial value. This seems to work, although it may not be the most elegant expression of the series.

Now I've decided that, given $\displaystyle n$ and $\displaystyle v_{n}$, I want to be able to calculate $\displaystyle v_{i}$. However solving my above equation for $\displaystyle v_{i}$ has left me going in circles.

I'd just as soon NOT get the answer - a gentle hint in the right direction will be appreciated, helpful, and will hopefully leave my pride intact.