Results 1 to 2 of 2

Math Help - Geometric series question

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    23

    Unhappy Geometric series question

    A large school board established a phone tree to contact all of its employees in case of emergencies. Each of the 3 superintendents calls 3 employees who each in turn calls 3 other employees and so on. How many rounds of phone calls are need to notify all 9840 employees?

    The back of the book says the answer is 8 rounds but I have no idea how to get that Please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello needhelpplease1
    Quote Originally Posted by needhelpplease1 View Post
    A large school board established a phone tree to contact all of its employees in case of emergencies. Each of the 3 superintendents calls 3 employees who each in turn calls 3 other employees and so on. How many rounds of phone calls are need to notify all 9840 employees?

    The back of the book says the answer is 8 rounds but I have no idea how to get that Please help
    After n rounds, the number of people contacted (including the original 3) is:
    3 + 3\times3+3\times3^2+3\times3^3...+3\times3^{n-1}
    which is a Geometric Series with:
    first term, a = 3; common ratio r = 3.
    The sum to n terms, S_n is given by:
    S_n = \frac{a(r^n-1)}{r-1}
    =\frac{3(3^n-1)}{2}
    We want S_n \ge 9840. So:
    \frac{3(3^n-1)}{2}\ge9840

    \Rightarrow 3^n-1\ge6560

    \Rightarrow n = 8
    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Geometric Series Question
    Posted in the Algebra Forum
    Replies: 8
    Last Post: December 11th 2011, 07:28 PM
  2. Superannuation Geometric Series Question
    Posted in the Business Math Forum
    Replies: 2
    Last Post: November 29th 2010, 07:57 PM
  3. Question about geometric series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 1st 2010, 04:07 PM
  4. Another Geometric Series Question.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 10th 2009, 01:11 PM
  5. Geometric and Arithmetic series question
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 30th 2008, 08:39 PM

Search Tags


/mathhelpforum @mathhelpforum