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Math Help - Find the function from a sequence.

  1. #1
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    Find the function from a sequence.

    There are two sequences I am unable to solve and any help on this matter would be appreciated.

    1,3,15,105,945,10395
    2,4,16,256,65536,4294967296
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  2. #2
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    I think the second sequence can be defined as

    when n = 1, the answer is 2
    when n > 1, f(n-1)^2

    I am still having problems with the first sequence
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    1)

    1
    1*3 = 3
    3*5 = 15
    15*7 =105
    105*9 =945
    945*11=10395
    Hence the
    T_{n+1} = T_{n} \times {2n-1}<br /> <br />
    2)
    2
    2^2=4
    4^2=16
    16^2=256
    256^2=65536
    65536^2=4294967296


    Hence
    T_{n+1} = (T_{n} ) ^2
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by vexiked View Post
    There are two sequences I am unable to solve and any help on this matter would be appreciated.

    1,3,15,105,945,10395
    Note here that:

    1*3 = 3
    3*5 = 15
    15*7 = 105
    105*9 = 945
    945*11 = 10395

    So we can say that if a_1=1, then a_{n+1}=(2n+1)a_n

    Does this make sense?

    2,4,16,256,65536,4294967296
    Note here that

    2^1=2
    2^2=4
    4^2=16
    16^2=256
    256^2=65536
    65536^2=4294967296

    Thus, if a_1=2, then a_{n+1}=(a_n)^2

    Does this make sense?
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  5. #5
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    Thank you all for you help! much appreciated!
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