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General formula of sequences

  1. Sep 2, 2012 #1
    Hi guys, I'm doing some exercises in which given a recursive sequence and its first term, I have to find the general formula/term. I am stuck in two and I would like some help. Thanks in advance. Now, the sequences:


    1) a1=1, an+1= an + ((-1)^(n+1))n^2

    So, the first terms are: a2=2, a3=-2, a4=7, a5=-9, a6=16

    Maybe you find it easy, I've been trying really hard to come up with the formula but I haven't got a clue.

    2) a1=1, an+1= an + n^3

    So, the first ones are: a2=2, a3=10, a4=37, a5=101

    And again, no idea.

    I suck at this, sorry to bother you but I would really appreciate your help.
     
  2. jcsd
  3. Sep 2, 2012 #2

    Ray Vickson

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    Use brackets. What you *wrote* says [itex]a_n + 1 = a_n + (-1)^{n+1} n^2,[/itex] but I am guessing meant [itex] a_{n+1} = a_n + (-1)^{n+1} n^2.[/itex] To do this in plain text, just say a_{n+1} or a_(n+1) instead of an+1, etc. Alternatively, you can use the "X2" button on the menu bar above the input panel; that would give an+1.

    Hint for 1): look at d_n = a_{n+1} - a_n = (-1)^(n+1) n^2 and note that
    a_n - a_1 = d_{n-1} + d_{n-2} + ... + d_1.

    RGV
     
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