Results 1 to 4 of 4

Math Help - Arithmetic progression and ratio of terms.

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    6

    Question Arithmetic progression and ratio of terms.

    Divide 32 into 4 parts which are in AP such that the ratio of the product of the extremes to the product of the means is 7:5 .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2009
    Posts
    277
    Thanks
    2
    If I'm interpreting your problem correctly, something is wrong in your problem.

    Consider the sequence:

    a-3d,a-d,a+d,a+3d

    This is an arithmetic progression with constant difference 2d.

    The product of the 2 outer terms is a^2 - 9d^2. The product of the 2 inner terms is a^2 - d^2.

    Your requested ratio is:
    \frac{a^2-9d^2}{a^2-d^2} = \frac {7}{5}

    which leads to
    -38d^2 = 2a^2

    which is impossible.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    6

    Unhappy

    But I got this problem in my exam
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    627
    Hello, prantik007!

    Please check the problem for typos.
    As stated, the situation is patently impossible.


    Divide 32 into 4 parts which are in AP such that the ratio of the product
    of the extremes to the product of the means is 7:5 .??

    The four parts are: . a,\;a+d,\;a+2d,\;a+3d

    The product of the extremes is: . P_E \:=\:a(a+3d) \:=\:a^2 + 3ad

    The product of the means is: . P_M \:=\:(a+d)(a+2d) \:=\:a^2 + 3ad + 2d^2

    . . It is obvious that: . P_E \:<\:P_M


    So how can . P_E:P_M \:=\:{\color{red}7:5} ?

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Arithmetic progression
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: January 7th 2010, 10:46 PM
  2. Arithmetic Progression or Arithmetic Series Problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 8th 2009, 12:36 AM
  3. Replies: 1
    Last Post: May 22nd 2009, 10:10 AM
  4. Replies: 8
    Last Post: March 23rd 2009, 07:26 AM
  5. Arithmetic progression
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 14th 2007, 05:37 PM

Search Tags


/mathhelpforum @mathhelpforum