1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Show that this sequence satisfies the recurrence relation

  1. Oct 31, 2012 #1
    1. The problem statement, all variables and given/known data
    Let d0, d1, d2,... be defined by the formula dn = 3n - 2n for all integers n ≥ 0. Show that this sequence satisfies the recurrence relation.

    dk = 5dk-1 - 6dk-2.

    2. Relevant equations

    3. The attempt at a solution

    I found that dk = 3k - 2k

    dk-1 = 3k-1 - 2k-1
    dk-2 = 3k-2 - 2k-2

    after plugging dk-1 and dk - 2 into the formula dk = 5dk-1 - 6dk-2, i am stuck and do not understand how to do the algebra if that is what i 'm supposed to be doing...any help?
  2. jcsd
  3. Oct 31, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    dk-1 = 3k-1 - 2k-1


    dk-2 = 3k-2 - 2k-2 '​
    Plug those into
    5dk-1 - 6dk-2 .​
    Do some algebra & see what you get.
  4. Oct 31, 2012 #3
    This is what i tried doing at i stated above...after you plug them in i get

    3k - 2k = 5( 3k-1 - 2k-1) - 6(3k-2 - 2k-2), I don't really understand what i can do with that algebraically...i must just be missing it...
  5. Oct 31, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    Use 3^(k-1)=3*3^(k-2) and 2^(k-1)=2*2^(k-2).
  6. Oct 31, 2012 #5
    ok so changing the equation to that gives me:

    5(3*3k-2 - 2*2k-2) - 6( 3k-2 - 2k-2)

    i can see how that gave me some like terms but multiplying through gives me:

    15 * 3k-2 - 10 * 2k-2 - 6 * 3k-2 - 6 * 2k-2

    i feel like that wasn't where you were leading me lol...i'm sorry, i'm not that great at algebra
  7. Oct 31, 2012 #6


    User Avatar
    Science Advisor
    Homework Helper

    I guess not. But you're almost there. Collect the 3^(k-2) terms. What do you get? And you've a sign error on the last term. Could you fix it?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook