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Thread: sequence

  1. #1
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    sequence

    What is the next number in the sequence: 1, 2, 3, 4, 5, 8, 7, 16, 9, ...?

    (A) 8 (B) 11 (C) 18 (D) 23 (E) 32
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by sri340 View Post
    What is the next number in the sequence: 1, 2, 3, 4, 5, 8, 7, 16, 9, ...?

    (A) 8 (B) 11 (C) 18 (D) 23 (E) 32
    While I'm sure you could justify any answer the one here is 32.

    Why?

    Write the sequence like this...

    $\displaystyle \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
    Term & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
    Value & 1 & 2 & 3 & 4 & 5 & 8 & 7 & 16 & 9 & ?
    \end{array}$

    Now look at ONLY the odd terms. What can you say about them?

    $\displaystyle \begin{array}{|c|c|c|c|c|c|}
    Term & 1 & 3 & 5 & 7 & 9 \\
    Value & 1 & 3 & 5 & 7 & 9
    \end{array}$

    Then look at the even terms.

    $\displaystyle \begin{array}{|c|c|c|c|c|c|}
    Term & 2 & 4 & 6 & 8 & 10 \\
    Value & 2 & 4 & 8 & 16 & ?
    \end{array}$

    It seems to be increasing...But by how much each time.
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  3. #3
    Senior Member Mukilab's Avatar
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    how would one find an nth term for this?
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  4. #4
    Super Member Deadstar's Avatar
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    Quote Originally Posted by Mukilab View Post
    how would one find an nth term for this?
    If $\displaystyle n$ is odd, nth term = $\displaystyle n$.

    If $\displaystyle n$ is even, call it $\displaystyle n=2k$.

    Then it's just $\displaystyle 2^k$
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