Question 740508
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Determine the common ratio of a geometric series that has these partial sums: S4= -3.5, S5= -3.75, S6= -3.875.
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Standard designations mean that S4 is the sum of the first 4 terms of this GP;

                                S5 is the sum of the first 5 terms of this GP;

                                S6 is the sum of the first 6 terms of this GP.


Therefore, the 5th terms is S5 - S4 = -3.75 - (-3.5) = -3.75 + 3.5 = -0.25;

           the 6th terms is S6 - S5 = -3.875 - (-3.75) = -3.875 + 3.75 = -0.125.


Now we can easily determine the common ratio of this GP.


It is the ratio of the 6th term to the 5th term

    {{{(-0.125)/(-0.25)}}} = 0.5.    <U>ANSWER</U>
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Solved.