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Math Help - Another Geometric Series Question.

  1. #1
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    Another Geometric Series Question.

    A geometric series has first term a and common ratio r. The sum of the first two terms of the geometric series is 7.2. The sum to infinity of the series is 20. Given that r is positive, find the values of r and a. [6]

    First I look at the sum to infinity and see that 20 - 20r = a

    And then I put 7.2 =  \frac{a (1 - r^2)}{(1 - r)}
    And subbing what I worked out above,  \frac{20 - 20r (1 - r^2)}{(1 - r)}

    And then I end up with 7.2 =  \frac{20 - 20r - 20r^2 - 20r^3}{(1 - r)}

    At this point I don't know what I'm doing now. Could someone please help?
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  2. #2
    MHF Contributor
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    Talking

    I think you're on the right track, but you maybe went slightly askew....

    From the formula for the sum of a geometric series, you have arrived at a\, =\, 20\, -\, 20r, where a is the first term of the series.

    Now use the fact that the second term is ar:

    . . . . . 20\, -\, 20r + (20\, -\, 20r)r\, =\, 20\, -\, 20r^2\, =\, 7.2

    Solve by square roots.
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