Results 1 to 3 of 3

Math Help - Recurrence relation

  1. #1
    Newbie
    Joined
    May 2008
    From
    Auckland, New Zealand
    Posts
    4

    Recurrence relation

    I have the following problem to solve:

    a_n = 4a_{n-1} - 4a_{n-2}
    where a_0 = -5 and a_1 = 3

    which I have attempted to solve via substitution, ie a_n = r^n

    When I do this, I end up with the result (r-2)^2 = 0
    hence, r = 2.

    When I put this back into the equation, I then get
    A + B = -5
    2A + 2B = 2(A + B) = 3
    => 0 = 13.

    What am I fumbling in here??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by ctwi001 View Post
    I have the following problem to solve:

    a_n = 4a_{n-1} - 4a_{n-2}
    where a_0 = -5 and a_1 = 3

    which I have attempted to solve via substitution, ie a_n = r^n

    When I do this, I end up with the result (r-2)^2 = 0
    hence, r = 2.

    When I put this back into the equation, I then get
    A + B = -5
    2A + 2B = 2(A + B) = 3
    => 0 = 13.

    What am I fumbling in here??
    When there are two distinct roots r_1 and r_2, the general solution has the form Ar_1 ^n + Br_2 ^n.

    But when r_1 = r_2=r ,the general solution is Ar^n + Bnr^n.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    From
    Auckland, New Zealand
    Posts
    4

    Thanks

    Thank you so much - I had been trying to come up with a pattern like that; and the text books etc didn't give that example of non-distinct roots.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Recurrence relation
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 15th 2011, 11:27 PM
  2. recurrence relation
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: October 18th 2010, 02:15 AM
  3. Recurrence Relation HELP
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: May 3rd 2009, 01:18 PM
  4. recurrence relation
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 15th 2009, 06:20 PM
  5. Recurrence relation
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 16th 2008, 08:02 AM

Search Tags


/mathhelpforum @mathhelpforum