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C1 sum question

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    Suggest the possible recurrence relationships for the following sequences:
    4, 10, 18, 38, 74
    I'm clueless on this one as it has no common or squaring or anything... but its meant to be
    Un+1 = 2Un + 2(-1)^k+1... how do I get to that??

    Also this one...
    For which values of x would the expression -8, x^2 and 17x from the first three terms of an arithmetic series?
    x = 1/2 and x = 8 ?????????

    Then final one....
    Find the sums of the following:
    3 + 7 + 11 + 14 + ... (20 terms)
    20th term is 820 it says but I don't get how or know how to do it...???

    Am I doing something wrong, I can do all of the 5 exercises except these 3 questions.

    Thanks whoever knows how to work them out.... I've been scratching head for the last 10 minutes thinking how to do.
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    (Original post by ckfeister)
    Suggest the possible recurrence relationships for the following sequences:
    4, 10, 18, 38, 74
    I'm clueless on this one as it has no common or squaring or anything... but its meant to be
    Un+1 = 2Un + 2(-1)^k+1... how do I get to that??

    Also this one...
    For which values of x would the expression -8, x^2 and 17x from the first three terms of an arithmetic series?
    x = 1/2 and x = 8 ?????????

    Then final one....
    Find the sums of the following:
    3 + 7 + 11 + 14 + ... (20 terms)
    20th term is 820 it says but I don't get how or know how to do it...???

    Am I doing something wrong, I can do all of the 5 exercises except these 3 questions.

    Thanks whoever knows how to work them out.... I've been scratching head for the last 10 minutes thinking how to do.
    First one is a nightmare admittedly, even with the answer it isn't obvious how you'd get to it, and to be honest, I don't know how you'd get to it.

    The second one, think of what a and d are and how you can use that given three terms (which in terms of a and d are...)

    The third one, I think you mean sum rather than 20th term.. for that one you can just apply the formula.
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    (Original post by ckfeister)
    Suggest the possible recurrence relationships for the following sequences:
    4, 10, 18, 38, 74
    I'm clueless on this one as it has no common or squaring or anything... but its meant to be
    Un+1 = 2Un + 2(-1)^k+1... how do I get to that??

    Also this one...
    For which values of x would the expression -8, x^2 and 17x from the first three terms of an arithmetic series?
    x = 1/2 and x = 8 ?????????

    Then final one....
    Find the sums of the following:
    3 + 7 + 11 + 14 + ... (20 terms)
    20th term is 820 it says but I don't get how or know how to do it...???

    Am I doing something wrong, I can do all of the 5 exercises except these 3 questions.

    Thanks whoever knows how to work them out.... I've been scratching head for the last 10 minutes thinking how to do.
    (i) 10 minutes isn't very long ..... get some paper out and chase ideas!
    (ii) 4, 10, 18, 38, 74

    rewrite as 4 , 2(4)+2 = 10 , 2(10)-2=18, 2(18)+2=38, 2(38)-2=74

    Hence ..... U1, 2(U1)+2, 2(U2)-2, 2(U3)+2, 2(U4)-2, ....

    Hence Un+1=2Un + ... well now you need to either +2 or -2 alternately ... you will notice from the line above that when n is odd you need to +2 and when n is even -2 ... hence we use(-1)^{n+1}

    Hence Un+1=2Un + 2 x (-1)^{n+1}
 
 
 
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