Solving Number Sequence

Discussion in 'High School' started by NoviceTutor, Jan 17, 2011.

  1. NoviceTutor

    NoviceTutor Companion

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    Jan 17, 2011

    Hello Forum,

    Given number sequence: 1, 2, 3, 6, 2, 8, 16, 2, 18, 36, 2, ... What would be the next 6 numbers in the sequence?

    I notice that the number 2 repeats. I also notice that 1x2=2, and 2x3=6. Then 8x2=16. Then 2 x 16=32. Then...I am stuck. I don't see the repeating pattern at all. Any suggestion at all is deeply appreciated.
     
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  3. TeacherGroupie

    TeacherGroupie Moderator

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    Jan 17, 2011

    I think the 1 doesn't belong, frankly, and I think you're acute to notice 2 x 3 = 6 and 2 x 8 = 16... but I think you meant 2 x 18 = 36.

    The other thing I notice is that 6 + 2 = 8, and 16 + 2 = 18. So I'd guess that 36 + 2 = 38 and then 2 x 38 = 7 and 76 + 2 = 78, so

    2, 3, 6, 2, 8, 16, 2, 18, 36, 2, 38, 76, 2, 78, 156, 2...
     
  4. TeacherGroupie

    TeacherGroupie Moderator

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    Jan 17, 2011

    (And it's a fairly ugly pattern, in my opinion.)
     
  5. NoviceTutor

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    Jan 18, 2011

    TG, you are exceptionally observant indeed. So first you add the first two terms to get the 3rd term and then you multiply the 3rd term by the second term to get the 4th term. Then the process repeats after 2 again. You are brilliant, TG. The pattern is then ADD, Multiply, repeat the process after 2. Thank you so much.
     
  6. TeacherGroupie

    TeacherGroupie Moderator

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    Jan 18, 2011

    One of our resident mathematicians has come up with something more elegant, but I'm too braindead to reproduce it right now.

    I just hope I haven't been doing someone's homework.
     
  7. Aliceacc

    Aliceacc Multitudinous

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    Jan 18, 2011

    Yeah, I'm kind of curious as to where this came from.
     
  8. NoviceTutor

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    Jan 18, 2011

    TG, you are doing a wonderful thing by sharing your knowledge so others will be in the light as you do. Since I am a tutor, I was asked to help solve this problem for one of the learners. I'm not sure if the person wanted to challenge me or what.
     
  9. NoviceTutor

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    Jan 18, 2011

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