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Can you solve this sequence?

  1. Mar 17, 2008 #1
    Here's something I thought of the other night:

    0, 1, 1, 1, 1, 5, 1, 7, 2, *, ?

    You don't need to know what * is :smile:.
     
    Last edited: Mar 17, 2008
  2. jcsd
  3. Mar 22, 2008 #2
    Numerators when a fraction is simplified and the denominator is 12, starting with 0.

    0/12=0 (0)
    1/12 (1)
    2/12 = 1/6 (1)
    3/12 = 1/4 (1)
    4/12 = 1/3 (1)
    5/12 (5)
    6/12 = 1/2 (1)
    7/12 (7)
    8/12 = 2/3 (2)
    9/12 = 3/4 (3) <---- That's the next one
    10/12=5/6 (5) <--- 5 is the one you're asking for

    The 100th number in your sequence:
    99/12 = 33/4 (33) Hence, you're right, I didn't need to know the 10th term.
     
    Last edited: Mar 22, 2008
  4. Apr 2, 2008 #3
    Actually drpizza,

    It's not necessarily 12. All you know is that 2^2*3 factors into the denominator, and 5, 7 and 2^3 don't. It could be 12*a, where a is any number not dividable by 2, 5 or 7. So you can't say what either the 10th or 100th terms are.

    But congratulations nonetheless :smile:
     
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