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Discrete mathematics: incursion

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data

    a 1= 2, a k+1, 2ak-1

    2. Relevant equations

    What is the 5th term

    3. The attempt at a solution

    a1= 2
    a2=2(2)-1= 3
    a3=2(3)-1=5
    a4=2(4)-1=7
    a5=2(5)-1=9

    5th term =9?
     
  2. jcsd
  3. Oct 16, 2008 #2

    Mark44

    Staff: Mentor

    Re: Discrete mathematics: recursion

    That would be recursion, not incursion, which has a very different meaning.
    The recursion formula you provided is wrong, and I guarantee you that it was not the one you were given in the problem.
    From the work you show later on, it appears that you meant this:
    a_1 = 2
    a_(k+1) = 2*a_(k) -1

    So,
    a_1 = 2
    a_2 = 2*a_1 -1 = 2(2) - 1 = 3
    a_3 = 2*a_2 -1 = 2(3) - 1 = 5
    So far, so good, but your next terms are wrong. Here's a hint:

    a_4 = 2*a_3 - 1 = 2(?) - 1
    a_5 = 2*a_4 - 1 = 2(?) - 1

    Mark
     
  4. Oct 16, 2008 #3
    That equation you presented was correct I did not know how to type it out properly.

    I see so

    a_4 = 2*a_3 - 1 = 2(?) - 1
    a_5 = 2*a_4 - 1 = 2(?) - 1

    a_4 = 2*a_3 -1 = 2(5) - 1 = 9

    a_5 = 2* a_4-1 = 2(9) -1 = 17

    Is that correct?
     
  5. Oct 16, 2008 #4

    Mark44

    Staff: Mentor

    Re: Discrete mathematics: REcursion

    Yep, it is.
     
  6. Oct 16, 2008 #5
    Thanks, for your help Mark!

    Syd
     
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