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Math Help - sequences and series geometric

  1. #1
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    Smile sequences and series geometric

    If the third and ninth temr of a geometric series with a positive common ratio are -3 and -192 repectively, determine the value of the first term a

    what formula would I use to answer this kind of question? how would I do this question?
    thanks for your help! I just need someone who can explain to me hwo I would approach this sort of question! thanks a lot!
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  2. #2
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    Quote Originally Posted by bobbluecow View Post
    If the third and ninth temr of a geometric series with a positive common ratio are -3 and -192 repectively, determine the value of the first term a

    what formula would I use to answer this kind of question? how would I do this question?
    thanks for your help! I just need someone who can explain to me hwo I would approach this sort of question! thanks a lot!
    We know that,
    Let a_1 be denoted by 'a' (first terms) then,
    a_3=r^2 a
    And,
    a_9=r^8 a
    Thus,
    r^8 a=-192
    r^2 a=-3
    Divide two equations,
    r^6=64=2^6
    Thus,
    r=2

    The third term is,
    -3=2^2 a
    Thus,
    a=-3/4
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