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if an is a geometric sequence where a1=4 and the sum of an=12. how would you find the common ratio of the sequence? please help

  • math -

    You must mean the infinite sum of ALL an, up to infinity. Partial sums cannot all be the same.

    Let the common ratio be x.
    4(1 + x + x^2 + ...) = 12
    (1 + x + x^2 + ...) = 3
    Now, recognize that the infinite series adds up to 1/(1-x).
    1/(1-x) = 3
    1/x = 1/3
    x = 2/3

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