Math

In a geometric series, t1=12 and S3=372. What is the greatest possible value for t5? Justify your answer.

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asked by Carol
  1. The formula for the sum of n terms with a common ratio of r is
    Sn=t1*(r^n-1)/(r-1)
    In particular, S3=372, t1=12

    (r^n-1)/(r-1)=S3/t1=31
    =>
    r=5, or r=-6

    case r=5
    t3=t1*r²=12*25=300

    case r=-6
    t3=t1*(-6)²=432

    Make your choice of the answer and justify.

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