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Thread: Next number in a sequence.

  1. #1
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    Next number in a sequence.

    Hello. This must be a silly question I guess but I have been trying to solve this but I simply cannot find any formula, so please someone help. Thank you.

    1,2
    1,25
    1,3333333333333333333333333333333
    1,5
    2
    x <------ so what is the next number after 2? Can you please also include the formula so I know how it is calculated? Thank you very much.
    Last edited by mr fantastic; November 25th 2010 at 11:31 AM. Reason: Re-titled.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Look by what number the first term is multiplied to to get teh second term and so on.

    You get first term times 25/24
    Second term times 16/15
    Third times 9/8
    Fourth times 4/3

    Can you find the pattern?
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  3. #3
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    I get Fifth times 1/0 (to get the sixth number) but I cannot devide with 0 ???
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Yes, I got the same problem. I guess that it's infinity...
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  5. #5
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    Hello, RAINERI!

    I agree . . . The answer is \dfrac{1}{0} . . . undefined.



    . . \begin{array}{c}1.2 \\ 1.25 \\ 1.\overline{3} \\ 1.5 \\ 2 \\ ? \end{array}

    What is the next number after 2?

    Write the numbers as fractions . . .

    . . \begin{array}{ccc} 1.2 &=& \dfrac{6}{5} \\ \\[-3mm] 1.25 &=& \dfrac{5}{4} \\ \\[-3mm]1.\overline{3} &=& \dfrac{4}{3} \\ \\[-3mm]1.5 &=& \dfrac{3}{2} \\ \\[-3mm] 2 &=& \dfrac{2}{1} \end{array}


    Note the pattern:

    . . \displaystyle \frac{6}{5} \;\to\;\frac{5}{4}\;\to\;\frac{4}{3} \;\to\;\frac{3}{2} \;\to\;\frac{2}{1} \;\to\;?

    The numerators are decreasing-by-one.
    The denominators are decreasing-by-one.

    The next fraction must be \dfrac{1}{0}

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