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Math Help - nth term

  1. #1
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    nth term

    This is something I should have learned in high school, but I never quite got it.

    Write down explicit formulate for the following sequences:

    1, 4, 36, 576, 14400, 518400 ...........

    For this, I squared rooted the numbers.. so I'm trying to find the pattern between:
    1, 2, 6, 24, 120, ...... but I can't find it. Is there a systematic approach to find the nth term for such a sequence? Obviously the arithmetic and geometric formulas won't work. But is there another logical way?

    And secondly, find the nth term of:

    3, 9, 18, 30, 48, 66, 87 ..........

    Now, again, I can see some sort of pattern. 9-3 = 6, 18-9 = 9, 30-18 = 12, =15, =18 etc. But I can't apply this.

    Please help. Thanks.
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  2. #2
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    This site can be very useful with this sort of problem.
    The On-Line Encyclopedia of Integer Sequences
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  3. #3
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    Thanks!

    How on earth did I miss the first one is (n!)^2 ?!

    But nothing came up for the second sequence, which was a bit odd.


    Any ideas?
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  4. #4
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    Hello, WWTL@WHL!

    The second one is baffling . . .


    Find the nth term of: .3, 9, 18, 30, 48, 66, 87, . . .

    We have: .3(1), 3(3), 3(6), 3(10), 3(16), 3(22), 2(29) , . . .

    We seem to have: 3 times a Triangular Number: . 3 \times \frac{n(n+1)}{2}
    . . but the fifth term breaks the pattern.


    The 5th, 6th and 7th terms seem to be: .3 (a Triangular Number plus 1)

    . . So what's going on?

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  5. #5
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    Sorry, the sequence should be:

    3, 9, 18, 30, 45, 63, .........

    I calculated it wrong, and you are right Soroban.

    Thank you very much!
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