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Math Help - 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...

    \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}<br />
Term & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\<br />
Value & 1 & 2 & 3 & 4 & 5 & 8 & 7 & 16  & 9 & ? <br />
\end{array}

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

    \begin{array}{|c|c|c|c|c|c|}<br />
Term & 1 & 3 & 5 & 7 & 9 \\<br />
Value & 1 & 3 & 5 & 7   & 9 <br />
\end{array}

    Then look at the even terms.

    \begin{array}{|c|c|c|c|c|c|}<br />
 Term & 2 & 4 & 6 & 8 & 10 \\<br />
 Value & 2 & 4 & 8 & 16   & ?<br />
 \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 n is odd, nth term = n.

    If n is even, call it n=2k.

    Then it's just 2^k
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