Formula for calculating profit

Question

I have 100 dollars. If I add 50% every day, on the first day, 150 dollars, the second day will be 225 dollars, and on the third day 337 dollars. Is there a formula for obtaining 337 dollars directly?

Answer 1

Your formula:

$$a_n=(1.5)^n\cdot 100$$

On the third day:

$$a_3=(1.5)^3\cdot 100$$

$$a_3=(3.375)\cdot 100$$