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Math Help - sequences by primitive recursive rules?

  1. #1
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    sequences by primitive recursive rules?

    a0 = 100
    an+1 = G(an,n) where G(x,n) = x-n

    what are the first four sequences?

    i realize a0=100
    and an(a0) +1 = 101
    but i do not understand the G(an,n) part or the G(x,n) parts........

    can someone explain how i get the answer without telling me, as i want to know how its done...thank you
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  2. #2
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    Quote Originally Posted by Apple8736 View Post
    a0 = 100
    an+1 = G(an,n) where G(x,n) = x-n

    what are the first four sequences?

    i realize a0=100
    and an(a0) +1 = 101
    but i do not understand the G(an,n) part or the G(x,n) parts........

    can someone explain how i get the answer without telling me, as i want to know how its done...thank you
    This looks to me like...

    a_0=100
    a_{n+1}=a_n-n

    a_1=a_0-0=100-0=100
    a_2=a_1-1=100-1=99
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