# Applying the Geometric Series Formula w/ This Real Life Situation?

It's #6.) in the following picture:

I know that this is a geometric series. Therefore, I planned on using the formula: $S_n$$= \frac{t_1(r^n-1)}{r-1} Where: S_n = sum of the first n terms r = common ratio n = the number of terms t_1 = first term I concluded that: S_n = 350 n = 2200 t_1 = 20 And I need to use the formula and what I know to calculate r, aka the portion of the profit per cup. Here's what I did: 350$$ = \frac{20(r^{2200}- 1)}{r-1}$

$(r-1) 350$$= 20(r^{2200}- 1) \frac{350r-350}{20}$$ =r^{2200}-1$

$350r-17.5$$=r^{2200}-1 350r-16.5$$ =r^{2200}$

$=r^{2200}-350r+16.5$

Basically I was trying to isolate $r$, but I know what I ended up with looks wrong.