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Math Help - Geometric Progression

  1. #1
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    Geometric Progression

    Hi guys, need help with this question please:

    The first term of a geometric series is 8. The sum of its first 10 terms is 1/8 of the sum of the reciprocal of these terms. Find the common ratio.
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  2. #2
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    Re: Geometric Progression

    Quote Originally Posted by Blizzardy View Post
    Hi guys, need help with this question please:

    The first term of a geometric series is 8. The sum of its first 10 terms is 1/8 of the sum of the reciprocal of these terms. Find the common ratio.
    x = geometric sum where a = 8, n = 10 and common ratio = r. Use the usual formula to get x in terms of r.

    y = geometric sum where a = 1/8, n = 10 and common ratio = 1/r. Use the usual formula to get y in terms of r.

    Substitute into x = (1/8)y and solve for r.
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    Re: Geometric Progression

    Quote Originally Posted by mr fantastic View Post
    x = geometric sum where a = 8, n = 10 and common ratio = r. Use the usual formula to get x in terms of r.

    y = geometric sum where a = 1/8, n = 10 and common ratio = 1/r. Use the usual formula to get y in terms of r.

    Substitute into x = (1/8)y and solve for r.
    Thanks for the reply!
    I substituted the values and ended up with this equation:
    8(1-r^10) / (1-r) = (1/64)(1-r^-10) / (1-r^-1)
    8/(1/64) = [(1-r^-10) / (1-r^-1)] / [(1-r^10) / (1-r)]

    But the solution just becomes more complicated, how do I continue?
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    Re: Geometric Progression

    Quote Originally Posted by Blizzardy View Post
    Thanks for the reply!
    I substituted the values and ended up with this equation:
    8(1-r^10) / (1-r) = (1/64)(1-r^-10) / (1-r^-1)
    8/(1/64) = [(1-r^-10) / (1-r^-1)] / [(1-r^10) / (1-r)]

    But the solution just becomes more complicated, how do I continue?
    You have \frac{8(1 - r^{10})}{1 - r} = \frac{1}{64} \frac{1 - \frac{1}{r^{10}}}{1 - \frac{1}{r}}

    My advice is to multiply the numerator and denominator of the right hand side of this equation by r^10. Then factorise the denominator, then look for common factors to cancel, simplify etc.

    I end up with the simple equation r^9 = - \frac{1}{8^3}
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