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    x^2, (8x+1) and (7x + 2), where x does not = 0, are the second, fourth and sixth terms respectively of an arithmetic series.

    a) Find the value of x

    I get a wrong answere, but I'm never sure on how to do these ones anyway so I'd be thankful for any help.

    Cheers.

    EDIT - Yes, I'm a ****ing idiot by writting the signs down wrong. Sorry for wasting your time for anyone who tried but I've now put up the correct question.
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    (Original post by Bebop)
    x^2, (8x-1( and (7x + 2), where x does not = 0, are the second, fourth and sixth terms respectively of an arithmetic series.

    a) Find the value of x

    I get a wrong answere, but I'm never sure on how to do these ones anyway so I'd be thankful for any help.

    Cheers.
    nth term = a + (n-1)d

    a + d = x^2
    a + 3d = 8x - 1
    a + 5d = 7x + 2

    (a + 3d) - (a + d) = (8x - 1) - x^2
    2d = 8x - 1 - x^2

    (a + 5d) - (a + 3d) = (7x + 2) - (8x - 1)
    2d = -x + 3

    8x - 1 - x^2 = -x + 3
    x^2 - 8x + 1 = x - 3
    x^2 - 9x + 4 = 0

    (x + (9/2))^2 - (81/4) + (16/4) = 0
    (x + (9/2))^2 - (65/4) = 0
    (x + (9/2))^2 = (65/4)
    x + (9/2) = (±√65)/2
    x = (±√65 - 9)/2

    Don't have a calculator to check that... looks wrong to me because you usually don't get a question with irrational roots and a series question at the same time.
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    yeah , thats wrong.
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    mm i use different method

    since 2,4,6th term common difference between these is 2d so it's same


    8x-1-x^2=7x+2-(8x-1)

    9x-4-x^2=0

    solve quadratic..


    get x = (-9±√65)/4

    looks weird.. x can be 2 values.
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    (Original post by Bebop)
    yeah , thats wrong.
    What's the right answer? I got the same quadratic equation as mika1 - I'm surprised it doesn't factorise for a p1 question. Is it definitely an arithmetic series not geometric?
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    (Original post by Bebop)
    yeah , thats wrong.
    really? i got x^2 - 9x + 4=0
    i noticed a mistake in mik1a's working.....when completing the square he put x+(9/2) instead of x-(9/2)....but the way you say it, seems like the answer is a long way off, not just a small mistake with the signs
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