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Math Help - [SOLVED] Formula for this sequence: 0,4,12,52,204,820

  1. #1
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    [SOLVED] Formula for this sequence: 0,4,12,52,204,820

    I'm to find an explicit formula for this sequence:

    a_1 = 0
    a_2 = 4
    a_3 = 12
    a_4 = 52
    a_5 = 204
    a_6 = 820
    ...

    (ie "add 1 and muliplty by 4; subtract 1 and multiply by 4; add 1 and muliplty by 4; subtract 1 and multiply by 4 etc etc")

    But can an explicit formula for a_n in terms of n (I don't want a "recurrent" formula based on a_(n-1), obviously) be found?
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  2. #2
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    answer to ur problem of series formula is here by shailesh k pandey.

    a(n)=4a(n-1) + 4 if n is odd
    a(n)=4a(n-1) - 4 if n is even
    with a(0)=0

    as i think you will find idt useful.
    e.g.
    a(1) = a(0)*4 + 4 = 0*4 + 4 = 4
    a(2) = a(1) *4 - 4 = 4*4 - 4 = 12 n is even
    and so on...
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    a(n) = \frac{(4^n + 4\times (-1)^n)}{5}
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  4. #4
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    secon ans

    nth term of series is as follows


    a(n)=(-1)^0*2^(2*n) + (-1)^1 * 2^(2*n - 2) +....while 2^0 not comes if it comes leave it

    e.g.
    a(0)=(-1)^0 * 2^(2*0) = 0
    a(1) = (-1)^0 * 2^(2*1) + (-1)^1 * 2^(2 - 2) but second will be igonered. = 4
    similarly:
    it follows for all other elements of the series.......
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  5. #5
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    shailesh1987 - look at ADARSH's post. He wrote a very nice solution that is concise and explicit.
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  6. #6
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    Thank u alot for suggestion.
    yes, I saw the ADARSH post that was really concise and explicit.
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