Sequences/Series Problem Based on Medication

  • Thread starter mundane
  • Start date
In summary, the patient takes 8 tablets on day 1, 7 on day 2, and then one tablet less each day until all tablets are gone. The patient has 8xmg of medication in their body after taking the 8th tablet.
  • #36
mundane said:
Awesome, thanks, SammyS!

For Tn, in part d) the equation I have is nxn-1+(n-1)xn-2 ... + but I don't know what to end it with. Do I call the number of days y and incorporate that in? I am trying to make it summation notation but can't get anywhere,

I assume that there would be enough (actually that's (n(n+1))/2 ) so that on the nth day, the patient would take 1 tablet.

So, I would still end with ... + 4x3 + 3x2 + 2x + 1 .
 
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  • #37
SammyS said:
I assume that there would be enough (actually that's (n(n+1))/2 ) so that on the nth day, the patient would take 1 tablet.

So, I would still end with ... + 4x3 + 3x2 + 2x + 1 .

I am kind of confused just because in this case it seems like n should be shown as the amount of tablets for part d.

Is that closed form that you've written above? It seems like a subjective term so I wasn't sure.
 
  • #38
I guess What I am trying to do is write it in summation notation for part d, but I don't know how to relate the last day's amount of n tablets. The only thing I can think of would be something (n-i
 
  • #39
I guess What I am trying to do is write it in summation notation for part d, but I don't know how to relate the last day's amount of n tablets. The only thing I can think of would be something (n-n+1)x^(n-n) if n is the initial amount of tablets and but I don't know how to sum that up properly...
 
  • #40
mundane said:
I am kind of confused just because in this case it seems like n should be shown as the amount of tablets for part d.

Is that closed form that you've written above? It seems like a subjective term so I wasn't sure.

mundane said:
I guess What I am trying to do is write it in summation notation for part d, but I don't know how to relate the last day's amount of n tablets. The only thing I can think of would be something (n-i
For parts (a), (b), and (c), you start with 8 tablets, then 7, then 6, ... then 2, then 1, for a total of 36 tablets.

If for part (d), the total number of tablets is not some value that gives you a final day dosage that follows the pattern then you have a real mess. In fact, even if you follow the pattern on the last day, if that dosage is not a single tablet, then with the information given you are left hanging. You are not told the total number of tablets.

So, I suggest again the there are enough total tablets prescribed so that on the last day (the nth day) the patient is given just one tablet.

That gives the patient n days worth of pills. The fact that it is suggested to use a subscript of n with the T, as in Tn, also suggests to me that the patent is given tablets for n days.
 
  • #41
SammyS said:
For parts (a), (b), and (c), you start with 8 tablets, then 7, then 6, ... then 2, then 1, for a total of 36 tablets.

If for part (d), the total number of tablets is not some value that gives you a final day dosage that follows the pattern then you have a real mess. In fact, even if you follow the pattern on the last day, if that dosage is not a single tablet, then with the information given you are left hanging. You are not told the total number of tablets.

So, I suggest again the there are enough total tablets prescribed so that on the last day (the nth day) the patient is given just one tablet.

That gives the patient n days worth of pills. The fact that it is suggested to use a subscript of n with the T, as in Tn, also suggests to me that the patent is given tablets for n days.

I definitely understan what you mean... But in the previous context would that mean that n=8 because there are 8 days? It seems like part d would be asking the same question as b then, right? Maybe I'm way off.

My teacher said that at part d) n should equal the initial number of tablets for Amy amount of days, say 25 for example, and we should make a closed form for how many pills in relation to # of days are left in the body at the last dose of 1 pill.
 
  • #42
mundane said:
...

d) A patient is prescribed n tablets of medication the first day, n-1 the second, and one tablet fewer each day until all tablets are gone. Write a formula that represent T(sub)n, the number of medication tablets in the body right after taking all tablets. Find a closed form for T(sub)n."
The above is a direct quote from your Original Post in this thread.

mundane said:
I definitely understand what you mean... But in the previous context would that mean that n=8 because there are 8 days? It seems like part d would be asking the same question as b then, right? Maybe I'm way off.

My teacher said that at part d) n should equal the initial number of tablets for Any amount of days, say 25 for example, and we should make a closed form for how many pills in relation to # of days are left in the body at the last dose of 1 pill.
Well, if n pills (tablets) are taken the first day (" n should equal the initial number of tablets for any amount of days ") and pills are taken every day for say, 25 days (for example), then if we are to diminish the dose by one pill each day, until the 25th day, when only one pill is taken, --- if all that is true, then the number of pills taken the first day, n, must be 25, for this example. Right?

This is what I stated previously. --- or what I intended ti state.

It is very much like the case of taking 8 pills the first day, etc. in part (b), but it is different. In part (d), n pills are taken the 1st day, one fewer is taken each subsequent day, until the nth day when one pill is taken. It's a generalization of part (b). Once you get your result, plugging in 8 for n, should give a result equivalent to the one obtained previously.
 
  • #43
SammyS said:
The above is a direct quote from your Original Post in this thread.


Well, if n pills (tablets) are taken the first day (" n should equal the initial number of tablets for any amount of days ") and pills are taken every day for say, 25 days (for example), then if we are to diminish the dose by one pill each day, until the 25th day, when only one pill is taken, --- if all that is true, then the number of pills taken the first day, n, must be 25, for this example. Right?

This is what I stated previously. --- or what I intended ti state.

It is very much like the case of taking 8 pills the first day, etc. in part (b), but it is different. In part (d), n pills are taken the 1st day, one fewer is taken each subsequent day, until the nth day when one pill is taken. It's a generalization of part (b). Once you get your result, plugging in 8 for n, should give a result equivalent to the one obtained previously.

Ohhh, so can I integrate it like you showed me for part b? And that closed form would show how to get T for any number of days?
 
  • #44
The one thing I don't get is how to express the last days. Thats why I asked about saying (n-i) Tablets since I didn't have a way to express the number of days, I guess.
 
  • #45
mundane said:
The one thing I don't get is how to express the last days. That's why I asked about saying (n-i) Tablets since I didn't have a way to express the number of days, I guess.

mundane said:
...

My teacher said that at part d) n should equal the initial number of tablets for Amy amount of days, say 25 for example, and we should make a closed form for how many pills in relation to # of days are left in the body at the last dose of 1 pill.

... at the last dose of one pill should answer your question above, in the first of the two quotes.

In post #42, I have given a fairly detailed version of my understanding of part (d). It's consistent with what your teacher said, and with the initial statement of the problem. Also, it's a more detailed version of my posts #34, #36 & #40, but with more detail and more complete.

To say it again, it appears to me that whatever number, n, of pills are taken the first day, there is a sufficient number of pills to follow the complete pattern & take one pill on day number n .

I can't make it any clearer than that.

*************************************

The steps in solving part (d) should be similar to the steps in solving part(b) .
 
<h2>1. What is a sequence/series problem based on medication?</h2><p>A sequence/series problem based on medication is a mathematical problem that involves the use of sequences or series to model and solve real-life medication-related scenarios. These problems may involve finding the dosage or effectiveness of a medication over time, calculating the cost of a medication over a certain period, or determining the optimal time to administer a medication for maximum effectiveness.</p><h2>2. How are sequences and series used in medication-related problems?</h2><p>Sequences and series are used in medication-related problems to model the behavior of a medication over time. Sequences are used to represent discrete events, such as the dosage of a medication at specific intervals, while series are used to represent continuous events, such as the gradually decreasing effectiveness of a medication over time.</p><h2>3. What are some common types of sequences/series problems in medication?</h2><p>Some common types of sequences/series problems in medication include finding the dosage of a medication at a specific time, calculating the total cost of a medication over a period, determining the optimal time to administer a medication for maximum effectiveness, and predicting the effectiveness of a medication over time based on its dosage and half-life.</p><h2>4. How can solving sequences/series problems in medication benefit patients and healthcare professionals?</h2><p>Solving sequences/series problems in medication can benefit patients and healthcare professionals by providing a more accurate and efficient way to manage medication dosages and treatment plans. By using mathematical models, healthcare professionals can make informed decisions about the dosage, timing, and cost of medications, leading to better patient outcomes and potentially reducing healthcare costs.</p><h2>5. What are some important factors to consider when solving sequences/series problems in medication?</h2><p>When solving sequences/series problems in medication, it is important to consider factors such as the half-life of the medication, the dosage and frequency of administration, any potential interactions with other medications, and the individual patient's response to the medication. It is also important to use accurate and up-to-date information, as well as appropriate mathematical models, to ensure the most effective and efficient solution.</p>

1. What is a sequence/series problem based on medication?

A sequence/series problem based on medication is a mathematical problem that involves the use of sequences or series to model and solve real-life medication-related scenarios. These problems may involve finding the dosage or effectiveness of a medication over time, calculating the cost of a medication over a certain period, or determining the optimal time to administer a medication for maximum effectiveness.

2. How are sequences and series used in medication-related problems?

Sequences and series are used in medication-related problems to model the behavior of a medication over time. Sequences are used to represent discrete events, such as the dosage of a medication at specific intervals, while series are used to represent continuous events, such as the gradually decreasing effectiveness of a medication over time.

3. What are some common types of sequences/series problems in medication?

Some common types of sequences/series problems in medication include finding the dosage of a medication at a specific time, calculating the total cost of a medication over a period, determining the optimal time to administer a medication for maximum effectiveness, and predicting the effectiveness of a medication over time based on its dosage and half-life.

4. How can solving sequences/series problems in medication benefit patients and healthcare professionals?

Solving sequences/series problems in medication can benefit patients and healthcare professionals by providing a more accurate and efficient way to manage medication dosages and treatment plans. By using mathematical models, healthcare professionals can make informed decisions about the dosage, timing, and cost of medications, leading to better patient outcomes and potentially reducing healthcare costs.

5. What are some important factors to consider when solving sequences/series problems in medication?

When solving sequences/series problems in medication, it is important to consider factors such as the half-life of the medication, the dosage and frequency of administration, any potential interactions with other medications, and the individual patient's response to the medication. It is also important to use accurate and up-to-date information, as well as appropriate mathematical models, to ensure the most effective and efficient solution.

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