Results 1 to 6 of 6

Math Help - Arithmetic Squence

  1. #1
    Newbie NoCrown's Avatar
    Joined
    Sep 2011
    Posts
    2

    Arithmetic Squence

    A doctor prescribes 200 mg of a medication on the first day, and the dosage is reduced by half every day, for one week. What is the total amount of medication prescribed?

    I know the answer, but the way I got the answer is definitely incorrect. This question was meant to be solved using an arithmetic or geometric equation, and although I know the majority of them, I seem to have forgotten the exact equation for solving a question like this. The correct answer is 397 mg. Can anyone help me?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2

    Re: Arithmetic Squence

    So there are seven days. Of course, if you just add up
    200
    100
    50
    25
    12.5
    6.25
    3.125
    You'll get about 397.
    The way to do this is with the sum

    S_n = \frac{n}{2}(a_1 + a_n)

    When n is the number of terms, and the a's are the first and last terms.

    So we have n = 7
    a_1 = 200
    a_n = a_7 = 3.125

    Compute.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie NoCrown's Avatar
    Joined
    Sep 2011
    Posts
    2

    Re: Arithmetic Squence

    Thank you very much. Is there an easier way to find the "n"th term?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2

    Re: Arithmetic Squence

    a_n = a_1 + (n - 1)d
    Where d is the signed difference between consecutive terms.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,659
    Thanks
    600

    Re: Arithmetic Squence

    Hello, NoCrown!

    A doctor prescribes 200 mg of a medication on the first day,
    and the dosage is reduced by half every day, for one week.
    What is the total amount of medication prescribed?
    Um, this is a geometric sequence.

    The first term is a = 200, the common ratio is r = \tfrac{1}{2}

    The sum of the first n terms is: . S_n \:=\:a\,\frac{1-r^n}{1-r}

    We have: . S_7 \:=\:200\,\frac{1-(\frac{1}{2})^7}{1-\frac{1}{2}} \:=\:200\,\frac{\frac{127}{128}}{\frac{1}{2}} \:=\:\frac{3175}{8} \;=\;396\tfrac{7}{8}\text{ mg.}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2

    Re: Arithmetic Squence

    Quote Originally Posted by Soroban View Post
    Hello, NoCrown!

    Um, this is a geometric sequence.

    The first term is a = 200, the common ratio is r = \tfrac{1}{2}


    The sum of the first n terms is: . S_n \:=\:a\,\frac{1-r^n}{1-r}

    We have: . S_7 \:=\:200\,\frac{1-(\frac{1}{2})^7}{1-\frac{1}{2}} \:=\:200\,\frac{\frac{127}{128}}{\frac{1}{2}} \:=\:\frac{3175}{8} \;=\;396\tfrac{7}{8}\text{ mg.}
    I have disgraced my family!
    (commits hari-kari)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Q in qeometric squence
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 05:01 AM
  2. A sum on arithmetic mean...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 30th 2010, 02:47 AM
  3. Arithmetic Progression or Arithmetic Series Problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 8th 2009, 12:36 AM
  4. Replies: 2
    Last Post: June 17th 2009, 01:25 PM
  5. a squence question
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: December 27th 2006, 11:45 PM

Search Tags


/mathhelpforum @mathhelpforum