1-st day, 8:00 am  in the morning. You take 20 mg of the medication.

Next day, (day 2), 7:59 am. Of these 20 mg, only 1-0.4 = 0.6 of 20 mg, i.e, 0.6*20 mg remained in your body.



          2-nd day, 8:00 am in the morning. You take 20 mg of the medication.

Next day, (day 3), 7:59 am. Of these 20 mg, only 1-0.4 = 0.6 of 20 mg, i.e, 0.6*20 mg remained in your body.

                            Also, 0.6 of the previous day (of the day 2) still remains in your body, i.e. 0.6*(0.6*20) = 0.6^2*20 mg

                            In all, 0.6*20 + 0.6^2*20 = 20*(0.6+ 0.6^2) mg of the medication is at this time in your body.


And so on, and so on.


Even with non-armed eyes, you just see now a sum of an geometric progression with the first term of 20 mg  and the common ratio of 0.6:


    (n+1)-th day, at 7:59 am, before taking the medication,  the amount of the medication in your body is  

              A = 0.6*20 + 0.6^2*20 + . . . + 0.6^n*20 = 20*(0.6 + 0.6^2 + . . . 0.6^n)


    (n+1)-th day, at 8:00 am, after taking the medication,  the amount of the medication in your body is  

              B = 20 + 0.6*20 + 0.6^2*20 + . . . + 0.6^n*20 = 20*(1+0.6 + 0.6^2 + . . . 0.6^n).


Both expressions A and B are the sums of geometric progressions.


So, by knowing the formula for the sum of geometric progressions, you can complete the solution on your own (!)