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Homework Help: Help reading a sequence.

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]a_{n+2}=3a_{n+1}-2a_n[/itex]
    [tex]a_1=1, a_2=1[/tex]
    Find the next 5 terms.

    2. Relevant equations



    3. The attempt at a solution
    I don't really understand the "a sub n" notation. Could someone do the next few terms so I can see how it's done?
     
  2. jcsd
  3. Apr 12, 2010 #2
    To find a3, for example, plug in n=1 into the first equation.

    So, let n=1. Then,
    a1+2 = a3 = 3a2 - 2a1 = 3(1) - 2(1) = 1
     
  4. Apr 12, 2010 #3
    [tex]a_{1+2}=3a_{1+1} + 2a_1[/tex]
    a_3 = 3(1)-2(1) = 1?
     
  5. Apr 12, 2010 #4

    Mark44

    Staff: Mentor

    The terms in the sequence are {a1, a2, a3, ..., an, an+1, an+2, ...}.

    The first formula says that to get the (n + 2)nd term in the sequence you need the preceding two terms, the (n + 1)st term and the nth term.
    Well, no, but maybe you can do them. You have a1 = 1 and a2 = 1. Use the first formula to get a3. Then when you have a3, use the formula again to find a4, and so on for as many terms as you need.
     
  6. Apr 12, 2010 #5
    So any possible a_n always equals 1?
     
    Last edited: Apr 12, 2010
  7. Apr 12, 2010 #6

    Mark44

    Staff: Mentor

    The formula is

    [tex]a_{1+2}=3a_{1+1} - 2a_1[/tex]
     
  8. Apr 12, 2010 #7

    Mark44

    Staff: Mentor

    For this sequence, yes.

    A simpler and nonrecursive definition would be an = 1 for n = 1, 2, 3, ...
     
  9. Apr 12, 2010 #8
    Ok, thank you. I kept thinking I was missing something because it's stupid to ask for the next 5 terms when they're all equal to 1.
     
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