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Math Help - Arithemetic Sequence question !!

  1. #1
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    Arithemetic Sequence question !!

    Hey, so i am confused about this question

    1. The common difference of an artimemetic sequence is 4. Show
    that :

    ÍS2n-2Sn =2n

    The funny O is a square root sign that extends untill the equals sign.


    Can somebody please help me !!
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  2. #2
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    Re: Arithemetic Sequence question !!

    AzraaBux

    revise the chapter of the arithmetic sequences and find the formula that gives the sum of n terms of an arithmetic sequence
    apply this formula twice ..
    once for 2n terms and second time for n terms. then subtract the two expressions and your answer will come very easily.

    dont forget that the 2nth term of the arithmetic sequence is a-(2n-1)4 while the nth term is a+(n-1)4 . a represents the first term of the sequence but it will cancel with the subtraction.
    I did it my self and it is easy...try it.
    MINOAS
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  3. #3
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    Re: Arithemetic Sequence question !!

    \begin{cases}S_n=\frac{n}{2}(2a_1+(n-1)d) \\S_{2n}=n(2a_1+(2n-1)d) \end{cases}

    therefore :

    \begin{cases}S_n=n(a_1+2(n-1)) \\S_{2n}=2n(a_1+2(2n-1)) \end{cases}

    hence :

    \sqrt{2n(a_1+2(2n-1))-2n(a_1+2(n-1))}=2n

    \sqrt{4n(2n-1)-4n(n-1)}=2n

    \sqrt{4n(2n-1-n+1)}=2n

    \sqrt{4n^2}=2n

    2n=2n
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  4. #4
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    Re: Arithemetic Sequence question !!

    Thanks so much Cool Kidds really appreaciate it
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  5. #5
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    Re: Arithemetic Sequence question !!

    I believe we should guide the students accordingly to do their HW and solve their questions rather than solve the HW for them.
    MINOAS
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