Compound discount

Question

I am trying to construct an equation for calculating a price, that takes into account compound interest of 10%.

1 item  = $10
2 items = $19
3 items = $27.1

so for a given number of items, I can calculate the price.

Answer 1

You are saying that the first item costs $10$, the second $10*0.9$, the third $10*0.9^2$. The total is then a geometric series: $10(1+0.9+0.9^2+\ldots 0.9^n)$ which sums to $10\left(\frac {1-0.9^{n}}{1-0.9}\right)$