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Found a series problem online, extremely hard to solve. help

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data


    What is the next number in the following series?
    1 2 12 48 216 936 4104 17928 78408 342792 ____________

    2. Relevant equations
    I haven't any idea


    3. The attempt at a solution

    power's of two, powers of three, prime numbers. I am beat

    it can be found on this test --->http://www.mental-testing.com/

    Mod's, I am sorry if this is in the wrong sub-directory. I couldn't figure out where else to put it.
     
    Last edited: May 29, 2012
  2. jcsd
  3. May 29, 2012 #2

    cepheid

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    All the numbers except the first two are divisible by 3.

    Start with the first two numbers in the sequence (1 and 2) as being given.

    Take 1 and double it: you get 2.

    Add this to 2: you get 4.

    Multiply the result by 3: you get **12**

    Repeat these three steps over and over again, just shifting your position in the sequence forward by one number each time. For example:

    2*2 = 4
    4 + 12 = 16
    16 * 3 = **48**

    12*2=24
    24+48 =72
    72*3 = **216**

    48*2 = 96
    96+216= 312
    312*3 = **936**

    etc.

    More generally, if ai is the ith number in the sequence, with a1 = 1 and a2 = 2, then:

    ai = 3 [2*ai-2 + ai-1 ] for i ≥ 3

    ai = 6ai-2 + 3ai-1

    EDIT: and by the way, "Pre-calculus Mathematics" would have been a good sub forum to post this thread in since 1) it is mathematics and 2) it is the type of math that comes before learning calculus.

    EDIT 2: based on this, I predict the next number in the sequence to be 1,498,824
     
    Last edited: May 29, 2012
  4. May 30, 2012 #3

    Borek

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    Staff: Mentor

    In the past similar questions landed in the brain teasers.
     
  5. May 30, 2012 #4

    cepheid

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    Good point Borek, especially since it didn't really seem like homework (else I would not have posted a full solution!)
     
  6. May 30, 2012 #5
    Thanks Cehpeid, I realized that every number was divisble by 2,3, and 12. I never thought to include the previous two terms.
     
    Last edited: May 30, 2012
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