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The sum of the 2nd and 5th terms of a geometric sequence is 3.5. The sum of the 3rd and 6th is -7. Determine the ratio r of the sequence and the first term a.

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3 answers
  1. ar + ar^4 = 7/2
    ar^2 + ar^5 = -7

    divide and you have

    r(1+r^3) / r^2(1+r^3) = -1/2
    1/r = -1/2
    r = -2
    So, a = 1/4

    Check. The sequence is

    1/4 -1/2 1 -2 4 -8
    -1/2 + 4 = 7/2
    1 + (-8) = -7

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  2. what are you dividing??

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  3. 5th term and 6th term

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