Results 1 to 4 of 4

Math Help - Progressions

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    202

    Progressions

    please help me on how to solve this question

    For a geometric progression,the first term is 6 and the sum of the 3 terms is 126.Find

    a)the possible values of the common ratio

    b)the 6th term of the geometric progression.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288
    G.P.:  \Sigma{ar^k}

    First term:6 \rightarrow{ar^0=6}
    Hence a=6

    I assume you mean 1st 3 terms
    a+ar+ar^2=126
    6r^2+6r+6=126
    r^2+r+1=21
    Solve this quadratic equation for your answer

    Part b
    6th term:  ar^5
    With value of a and r, insert for answer
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,700
    Thanks
    454
    Quote Originally Posted by mastermin346 View Post
    please help me on how to solve this question

    For a geometric progression,the first term is 6 and the sum of the 3 terms is 126.Find

    a)the possible values of the common ratio

    b)the 6th term of the geometric progression.
    a) 6 + 6r + 6r^2 = 126

    solve for r (note that there will be more than one solution)

    b) 6th term is 6r^5
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    For a geometric progression,the first term is 6 and the sum of the 3 terms is 126.Find
    a)the possible values of the common ratio
    The nth partial sum is S_{n}=a_{1}\cdot \frac{1-r^{n}}{1-r}

    So, the sum of the first 3 terms is given as S_{3}=126 and the first term is a_{1}=6

    Solve 126=6\cdot \frac{1-r^{3}}{1-r}\Rightarrow 126=6(r^{2}+r+1) for r.

    b)the 6th term of the geometric progression.
    Just use a_{n}=a_{1}r^{n-1} once you find r.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. progressions!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 20th 2010, 04:41 PM
  2. Progressions
    Posted in the Statistics Forum
    Replies: 3
    Last Post: June 2nd 2010, 02:46 PM
  3. Progressions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 1st 2010, 07:31 PM
  4. Progressions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 23rd 2009, 08:38 AM
  5. please help with progressions :)
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 30th 2006, 08:26 AM

Search Tags


/mathhelpforum @mathhelpforum