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the third term of a geometric sequence is t3= -75 and the sixth term is t6= 9375. determine the first term and the common ratio

  • math -

    For a geometric series,
    the nth term is
    t(n)=arn

    So
    t(3)=ar³
    t(6)=ar6
    t(6)/t(3)
    = ar6 / ar³
    = r6-3
    = r³

    Solve for r in
    r³=9375/(-75)
    r=(-125)1/3
    =-5

    A = t(3)/r³
    = -75/(-5)³
    = 3/5

    and first term
    = t(1)
    = Ar
    = 3/5(-5)
    = -3

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