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Math Help - Arithmetic Series Question

  1. #1
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    Arithmetic Series Question

    The sum of the first 5 terms of an arithmetic series is 85, and the sum of the first 6 terms is 123. Write the first 3 terms of the series.

    Okay i tried, but ended up with strange numbers.

    formulas:
    tn=t1+(n-1)d
    sn=n/2(2(t1)+(n-1)d)

    please help
    Last edited by Vince604; November 18th 2012 at 01:14 AM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Arithmetic Series Question

    Using the summation formula, we find:

    S_5=\frac{5}{2}(2t_1+4d)=85

    S_5=3(2t_1+5d)=123

    The two equations may be written:

    t_1+2d=17

    2t_1+5d=41

    Now, solve this system to determine t_1 and d.
    Thanks from Vince604
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  3. #3
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    Re: Arithmetic Series Question

    thanks Mark, helpful as always. i try later, too tired now...
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  4. #4
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    Re: Arithmetic Series Question

    Quote Originally Posted by MarkFL2 View Post
    Using the summation formula, we find:

    S_5=\frac{5}{2}(2t_1+4d)=85

    S_5=3(2t_1+5d)=123

    The two equations may be written:

    t_1+2d=17

    2t_1+5d=41

    Now, solve this system to determine t_1 and d.

    answer is d=7 t1=3

    I actually wrote it out exactly like you did, but then i got help from another site as well and the person said that i could bring the fraction (5/2 & 6/2) over and use it to divide with 85 and 123. whew. I made it seem so difficult lol.

    I blame my teacher for not showing the proper steps!!!

    Oh and the two equations with 17 and 41 confuses me, so i didn't know what to do with them.
    Last edited by Vince604; November 18th 2012 at 04:45 PM.
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Arithmetic Series Question

    Given the system:

    (1) t_1+2d=17

    (2) 2t_1+5d=41

    I would multiply (1) by -2, then add the two equations to eliminate t_1:

    d=7

    and then using (1), we find:

    t_1=3
    Thanks from Vince604
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  6. #6
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    Re: Arithmetic Series Question

    Quote Originally Posted by MarkFL2 View Post
    Given the system:

    (1) t_1+2d=17

    (2) 2t_1+5d=41

    I would multiply (1) by -2, then add the two equations to eliminate t_1:

    d=7

    and then using (1), we find:

    t_1=3
    OHHH, so you try to eliminate what you can to solve right?
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Arithmetic Series Question

    Yes, elimination is one way, substitution is another. I tend to favor elimination for small systems like this.
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    Re: Arithmetic Series Question

    Thanks
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