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!

Induction Proof: Am I on the right track?

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Let a(1)=a(2)=5 and a(n+1)=a(n)+6a(n-1), n≥2
    Use induction to prove that a(n)=(3^n)-(-2)^n for n≥1

    2. Relevant equations

    Not applicable

    3. The attempt at a solution

    I have check that a(3) = 5+6·5 = 35 = 3^3-(-2)^3 so it holds for n = 3.
    The cases n = 1 and n = 2 are similar and also hold

    So I assumed that it holds for n and considered

    a(n+1) = a(n)+6a(n-1)
    = (3^n-(-2)^n)+6(3^(n-1)-(-2)^(n-1))

    The second term [6(3^(n-1)-(-2)^(n-1))] equals [2·3^n+3·(-2)^n].

    So,

    a(n+1) = (3^n-(-2)^n)+(2·3^n+3·(-2)^n)
    = 3^(n+1)-(-2)^(n+1)

    Is this a valid induction proof? Am I on the right lines here?

    Thanks!
     
  2. jcsd
  3. Mar 8, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hi elizaburlap! welcome to pf! :smile:

    (try using the X2 and X2 buttons just above the Reply box :wink:)
    yes, that's all (difficult to read :wink:, but) fine! :smile:
     
  4. Mar 8, 2012 #3
    Thank you! This was my first attempt at an induction proof, so I wasn't too sure.

    Oh! I see the x2 now, thanks :)
     
  5. Mar 10, 2012 #4
    Math1115. (:p)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Induction Proof: Am I on the right track?
  1. Am i doing this right (Replies: 4)

  2. Am i right here? (Replies: 0)

  3. Am I doing this right? (Replies: 1)

Loading...