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.
The answer in the book is $0.15 per cup.
I'm assuming that my approach might've been wrong? What exactly did I do wrong?
