# Thread: I want to know how to set up this equation.

1. ## I want to know how to set up this equation.

So say I have to take this medication, I have 9600mg total. I have to take 120mg's every day for the first week. And for each week after that I have to add 40mg more. So it would be 120mg's per day for the first week, 160mg per day for the second week ect.. ect..

What I want to know is how to set up an algebraic equation that will show me how many days I will be taking this medication for until it is gone.. Now Ive already figured it out in a childish 6th grader manner and I know that the answer is 43 days. This is how I did it:

9600mg Total

120mg/day/week, 840mg, week 1

160mg/day/week, 1120mg, week 2

200mg/day/week, 1400mg, week 3

240mg/day/week, 1680mg, week 4

280mg/day/week, 1960mg, week 5

320mg/day/week, 2240mg, week 6

Finally. 360mg for 1 day = 9600mg total.

6 weeks and 1 day. 43 days.

I had to figure out for each weak individually but I KNOW there is has to be some kind of equation for this I just have NO idea how to set it up with the sum of how many mg's I have to take changing every week. So if anyone can figure it out that would be awesome.

2. Originally Posted by Psymon
So say I have to take this medication, I have 9600mg total. I have to take 120mg's every day for the first week. And for each week after that I have to add 40mg more. So it would be 120mg's per day for the first week, 160mg per day for the second week ect.. ect..

What I want to know is how to set up an algebraic equation that will show me how many days I will be taking this medication for until it is gone.. Now Ive already figured it out in a childish 6th grader manner and I know that the answer is 43 days. This is how I did it:

9600mg Total

120mg/day/week, 840mg, week 1

160mg/day/week, 1120mg, week 2

200mg/day/week, 1400mg, week 3

240mg/day/week, 1680mg, week 4

280mg/day/week, 1960mg, week 5

320mg/day/week, 2240mg, week 6

Finally. 360mg for 1 day = 9600mg total.

6 weeks and 1 day. 43 days.

I had to figure out for each weak individually but I KNOW there is has to be some kind of equation for this I just have NO idea how to set it up with the sum of how many mg's I have to take changing every week. So if anyone can figure it out that would be awesome.
HI

notice that this forms a AP

840 , 1120 , 1400 , ...

where a=840 and d=280 , Sn=9600

so 9600=n/2[2(840)+(n-1)(280)]

You will find that n is 6.1499 .

That means you need 6.1499 weeks to complete the medication which is approximately 43 days .