1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quadratic Recurrence Relation

  1. Jul 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Dang it! More recurrence relation problems, but this time it’s due to a quadratic equation.

    Q. In the sequence u1, u2, u3,…,un,
    u1 = 0, u2 = 3, u3 = 12 and un = a + bn + cn2
    Find the values of a, b and c.

    2. Relevant equations

    Provided at back of book…
    Answer: a = 3, b = -6, c = 3

    3. The attempt at a solution

    Attempt:
    If n = 1 then u1 = a + b(1) + c(1)2 = 0
    = a + b + c = 0
    If n = 2 then u2 = a + b(2) + c(2)2 = 3
    = a + 2b + 4c = 3
    If n = 3 then u3 = a + b(3) + c(3)2 = 12
    = a + 3b + 9c = 12

    Each value of un is a multiple of 3, hence the answers (a, b and c) are also multiples of 3, so I’m guessing that I need to use some kind of ratio solution between each new quadratic to find the answer. The difficulty I’m having is that other quadratic equations I’ve solved for already had values for the coefficients, so I’m uncertain on what quadratic formula I need at this point. I probably don’t need one, but I’m definitely stuck either way.
     
  2. jcsd
  3. Jul 17, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Hi odolwa99! :smile:

    There is no need for quadratic formula's. You have a system of three equations and three unknowns:

    a + b + c = 0
    a + 2b + 4c = 3
    a + 3b + 9c = 12

    Solve it.
     
  4. Jul 17, 2011 #3
    Ok, thanks for the tip. I'll give it a second look.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quadratic Recurrence Relation
  1. Recurrence Relation (Replies: 1)

  2. Recurrence relations (Replies: 1)

  3. Recurrence Relations (Replies: 4)

  4. Recurrence relation (Replies: 2)

  5. Recurrence relation (Replies: 5)

Loading...