When doctors prescribe medicine at equally spaced time intervals, they are aware that the body metabolizes the drug gradually. after some period of time, only a certain percent of the original amount remains. after each dose, the amount of the drug in the body is equal to the amount of the given dose plus the amount remaining from the previous doses. the amount of the drug present in the body after the nth dose is modelled by a geometric series where t1 is the prescribed dosage and r is the previous dose remaining in the body. suppose a person with an ear infection takes a 200-mg ampicillin tablet every 4 h. about 12% of the drug in the body at the start of a four-hour period is still present at the end of that period. what amount of ampicillin is in the body, to the nearest tenth of a milligram, a) after taking the third tablet? b) after taking the sixth tablet?

The situation in question looks like this.ingest a tablet and we have this much of the medication in the body.    after four hours, we take another tablet, but the previous tablet amount is reduced to 12% of its amount. the previous gets multiplied by 0.12 while we add 200. the sum of those amounts is the amount of medication after four hours:     elapse another four hours. pop in a new tablet. the very first tablet gets its value decreased again by 12%. the second tablet ingested gets its first 12% decrease.    from this demonstration and the question text, the amount of medication in the body  can be modeled by a geometric series. it's just that we work backwards in time, i.e. the first term in the series  comes from the latest tablet ingested and the last term in the series is from the very first tablet ingested."first" term: 200common ratio: 0.12formula for sum of a geometric series with n terms, common ratio r, and first term a1:     ======a)answer: 226.88 mgthird tablet means sum up three terms    ======b)answer:   227.27 mgsixth tablet means sum up 6 terms