What is the correct mathematical symbolism for expressing how many times I have to subtract a variable number from a given starting point? Say that I have 1000 dollars that I need to collect. I know that on the first day my income is 20 dollars, one the second it's 30 dollars and so on, on every subsequent day my income increases by 10 dollars. I also know that on every day I save 80% of my income. How would I express calculating how many days it takes until I have 1000 dollars saved?
The operation would be: ((((1000 - 20 * 0.8) - 30 * 0.8) - 40 * 0.8) - 50 * 0.8) ....
And I would like to count how many times I have to do this subtraction before I reach 0.
I know how I would do this algorithmically/programmatically, just making a loop that adds to some counter every time it runs and stops when it gets to 0, but I'm not sure how to express this as a mathematical equation. What would be the correct way to do it?

You need to compute
$$0.8 \left(\sum_{i=0}^n \left(20+10i\right)\right)=8 \left(2n+\frac{(n+1)n}{2}\right)$$
and then equate to $1000$. Therefore, you have to solve
$$1000=8 \left(2n+\frac{(n+1)n}{2}\right)$$
I get $n=\frac{5}{2}\left(\sqrt{41}-1\right)\approx 13.5.$
