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Maths Questions (GCSE)

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    hey
    i've got a few maths problems that i cant seem to solve

    Sequences and formulae:

    find the value of n for which u has the given value in these:

    1. u = 2n u = 256 answer: 8
    2. u = 3n u = 2187 answer: 7
    3. u = n(n-1) u = 380 answer: 20


    And then, how to work out the formula for

    1. 1/2, 1/3, 1/4
    2. 2, 1.5, 1.333333, 1.25
    3. 1, 2/3, 3/5, 4/7, 5/9


    thanks a lot
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    (Original post by koldtoast)
    hey
    i've got a few maths problems that i cant seem to solve

    Sequences and formulae:

    find the value of n for which u has the given value in these:

    1. u = 2n u = 256 answer: 8
    2. u = 3n u = 2187 7
    3. u = n(n-1) u = 380 20


    And then, how to work out the formula for

    1. 1/2, 1/3, 1/4
    2. 2, 1.5, 1.333333, 1.25
    3. 1, 2/3, 3/5, 4/7, 5/9


    thanks a lot
    Which types of series are these? Geometric or arithmetic?
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    (Original post by koldtoast)
    And then, how to work out the formula for

    1. 1/2, 1/3, 1/4
    2. 2, 1.5, 1.333333, 1.25
    3. 1, 2/3, 3/5, 4/7, 5/9


    thanks a lot
    i dunno bout the first lot, but i can try these

    for fractions u hav to seperate the top and bottom

    1)so 1/2, 1/3, 1/4 would be

    1/n-1

    2)2/1, 3/2, 4/3, 5/4 is the 2nd question in fraction form

    so it would be n+1/n

    3) 1, 2/3, 3/5, 4/7, 5/9

    woulkd be n/the formula for odd numbas...which i cant seem to rememba...or wrk out at the moment!

    let me know if ya need explainin on the above 2
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    (Original post by Jonatan)
    Which types of series are these? Geometric or arithmetic?
    the 2nd lot look like arithmetic!

    the first...iu dunno
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    For the first, since its GCSE, you have to use trial and error.
    256 = 2^n, try a few numbers and eventually get the right one.

    For 3,
    380 = n(n-1)
    380 = n^2 - n
    0 = n^2 - n - 380, which you can solve.
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    (Original post by koldtoast)
    h
    And then, how to work out the formula for

    1. 1/2, 1/3, 1/4
    2. 2, 1.5, 1.333333, 1.25
    3. 1, 2/3, 3/5, 4/7, 5/9


    thanks a lot
    1.) nth term = 1/(n+1)
    2.) nth term = (n+1)/(n)
    3.) nth term = (n)/(2n-1)
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    (Original post by JamesF)
    For the first, since its GCSE, you have to use trial and error.
    256 = 2^n, try a few numbers and eventually get the right one.

    For 3,
    380 = n(n-1)
    380 = n^2 - n
    0 = n^2 - n - 380, which you can solve.
    er, i dunno how to solve that lol
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    (Original post by koldtoast)
    hey
    i've got a few maths problems that i cant seem to solve

    Sequences and formulae:

    find the value of n for which u has the given value in these:

    1. u = 2n u = 256 answer: 8
    2. u = 3n u = 2187 answer: 7
    3. u = n(n-1) u = 380 answer: 20


    And then, how to work out the formula for

    1. 1/2, 1/3, 1/4
    2. 2, 1.5, 1.333333, 1.25
    3. 1, 2/3, 3/5, 4/7, 5/9


    thanks a lot
    OK thanks i've figured out the second lot of questions involving fractions, but i just can't understand the first question (to do with sequences)

    1. u = 2n u = 256 answer: 8
    the way i see it....

    256 = 2n
    n = 128

    i just dont see how the answer can end up being 8?
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    (Original post by koldtoast)
    er, i dunno how to solve that lol
    n^2 - n - 380 = 0

    Using the quadratic formula:

    a = 1, b = -1, c = -380

    n = {1(+/-)sq.root [(-1)^2 - (4*1*-380)]}/2

    n = [1 (+/-) sq.root (1 + 1520)]/2

    n = [1 + sq. root (1521)]/2 = 20 OR
    n = [1 - sq.roo t(1521)]/2 = -19

    Solutions: n = 20 OR n = -19
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    (Original post by koldtoast)
    OK thanks i've figured out the second lot of questions involving fractions, but i just can't understand the first question (to do with sequences)

    1. u = 2n u = 256 answer: 8
    the way i see it....

    256 = 2n
    n = 128

    i just dont see how the answer can end up being 8?
    It isn't supposed to be 2n, it is supposed to be 2^n

    2^8 = 256

    You must have copied it down wrong.
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    (Original post by koldtoast)
    OK thanks i've figured out the second lot of questions involving fractions, but i just can't understand the first question (to do with sequences)

    1. u = 2n u = 256 answer: 8
    the way i see it....

    256 = 2n
    n = 128

    i just dont see how the answer can end up being 8?
    I thought you had just mis-read the question, if it said
    u = 2^n ( 2 to the power n)
    Then 8 would be the correct answer.

    Btw to solve 3, if you cant solve quadratic equations, then like the others, you will need to use trial and improvement.
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    (Original post by JamesF)
    I thought you had just mis-read the question, if it said
    u = 2^n ( 2 to the power n)
    Then 8 would be the correct answer.

    Btw to solve 3, if you cant solve quadratic equations, then like the others, you will need to use trial and improvement.
    You do quadratic equations at GCSE. We learnt that formula at GCSE, it came up in the exam as well.
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    (Original post by koldtoast)
    OK thanks i've figured out the second lot of questions involving fractions, but i just can't understand the first question (to do with sequences)

    1. u = 2n u = 256 answer: 8
    the way i see it....

    256 = 2n
    n = 128

    i just dont see how the answer can end up being 8?
    i think the question is supposed to be 2^n rather than 2n.
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    (Original post by Undry1)
    i think the question is supposed to be 2^n rather than 2n.
    Yep.
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    (Original post by bono)
    n^2 - n - 380 = 0

    Using the quadratic formula:

    a = 1, b = -1, c = -380

    n = {1(+/-)sq.root [(-1)^2 - (4*1*-380)]}/2

    n = [1 (+/-) sq.root (1 + 1520)]/2

    n = [1 + sq. root (1521)]/2 = 20 OR
    n = [1 - sq.roo t(1521)]/2 = -19

    Solutions: n = 20 OR n = -19
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    hmm, i'm typing it straight out of the book, which btw is the Edexcel GCSE Maths Higher Course book for 2001 specs... page 292 exercise 14b

    Q8. u = 2n u= 256
    Q9. u = 3n u= 2187
    Q10.u = n(n-1) u= 380
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    (Original post by koldtoast)
    hmm, i'm typing it straight out of the book, which btw is the Edexcel GCSE Maths Higher Course book for 2001 specs... page 292 exercise 14b

    Q8. u = 2n u= 256
    Q9. u = 3n u= 2187
    Q10.u = n(n-1) u= 380
    Yes, but I bet it's a "2 with a small little n next to the top of it" not 2n.

    Can't you see it's "2^" ?
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    2^n makes sense, and that is what the answer at the back would seem to support.

    its weird but it REALLY looks like 2n instead of 2^n (with a little n towards the top right of the '2')... :confused: i'll see if i can scan the page somehow or something
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    (Original post by koldtoast)
    2^n makes sense, and that is what the answer at the back would seem to support.

    its weird but it REALLY looks like 2n instead of 2^n (with a little n towards the top right of the '2')... :confused: i'll see if i can scan the page somehow or something
    Well obviously, as 2^n = 256.

    If you can, scan in the page, i'd be interested to see it.
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    I just checked in my book and he/she is right the question is as they typed it...
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