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Math Help - Recurrence Sequences

  1. #1
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    Recurrence Sequences

    A sequence of terms {U_n} is defined by n\geq1 by the recurrence relation U_{n+1}=kU_n+2, where k is a constant. Given that U_1=3:

    a) Find an expression in terms of k for U_2.


    Please tell me how to do this .
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  2. #2
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    Quote Originally Posted by Viral View Post
    A sequence of terms {U_n} is defined by n\geq1 by the recurrence relation U_{n+1}=kU_n+2, where k is a constant. Given that U_1=3:

    a) Find an expression in terms of k for U_2.


    Please tell me how to do this .
    Let n = 1 in U_{n+1}=kU_n+2, so

    U_{2}=k U_1+2 = 3k + 2.
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  3. #3
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    part b says "hence find an expression for U_3". The answer is 3k^2+2k+2 but I have no idea how to get this answer. Do you know of any notes on the internet with recurrence sequences?
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    Quote Originally Posted by Viral View Post
    part b says "hence find an expression for U_3". The answer is 3k^2+2k+2 but I have no idea how to get this answer. Do you know of any notes on the internet with recurrence sequences?
    Since U_{n+1} = k U_n +2 then substitute n = 2 so

    U_3 = kU_2 + 2 but you already know U_2 = 3k +2 from the first part.

    You might try googleing it on the web. Like I did to get this site

    Difference Equation Tutorial

    Try the word "difference equation".
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