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Math Help - Arithmetic Sequence

  1. #1
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    Arithmetic Sequence

    For a positive integer, consider the arithmetic sequence:

    n, n+19, n+38, n+57,.......

    The number 2013 may or may not belong to the sequence. What is the smallest positive integer n such that 2013 does belong to the sequence?

    A) 4 B) 7 C) 11 D) 14 E) 18

    Please explain how you got the answer.
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  2. #2
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    Re: Arithmetic Sequence

    Quote Originally Posted by ConnieLam View Post
    For a positive integer, consider the arithmetic sequence:

    n, n+19, n+38, n+57,.......

    The number 2013 may or may not belong to the sequence. What is the smallest positive integer n such that 2013 does belong to the sequence?

    A) 4 B) 7 C) 11 D) 14 E) 18

    Please explain how you got the answer.
    This sequence is $\{x: x=n+19k, k\in \mathbb{N}$

    Divide 2013 by 19 to get

    $2013 = 105 \times 19 +18$

    Thus 18 will be the smallest $n$ such that 2013 is an element of the sequence.
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  3. #3
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    Re: Arithmetic Sequence

    use formula for AP

    a(m)=a+(m-1)d
    =n+(m-1)19
    now here we have to find n
    so here if m=106
    (m-1)*19=1995
    and a(m)=2013 so m=106
    if m=107 n=-1 which is not possible
    so n=18
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