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:

Where

is the nth value and

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

and

, I want to be able to calculate

. However solving my above equation for

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.