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Math Help - 2, 5, 8, 11, 14... (q2)

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    2, 5, 8, 11, 14... (q2)

    Sequence given: 2, 5, 8, 11, 14...

    Prove that the product of any two consecutive numbers in the sequence can't be in the sequence?
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  2. #2
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    Quote Originally Posted by Natasha
    Sequence given: 2, 5, 8, 11, 14...

    Prove that the product of any two consecutive numbers in the sequence can't be in the sequence?
    The sequence is arithmatic, with a separation of 3 and initial value of 2. So we may model the series as a_{n}=3n+2.

    We want to multiply two consecutive numbers in the series, so use the n and (n+1) terms:
    a_{n+1} * a_n =(3(n+1)+2)(3n+2)=(3n+5)(3n+2)
    =9n^2+21n+10
    If this is a member of the series, then (3q+2)=9n^2+21n+10 for some integer q. Solving for q we obtain:
    q=3n^2+7n+8/3 which is never an integer for any n.

    -Dan
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    Because each number has form,
    3k+2
    If multiplied together they produce, (of form)
    3k+1
    Impossible by definition of this sequence.
    Q.E.D.
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