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    Thanks:

    Find the number of terms in this geometric series

    8/81 -4/27 + 2/9......-1 11/16 ( thats meant to be -1 and 11/16)

    You cant use logs this time so how do you do it. I just can't thinK!
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    (Original post by MAC1205)
    Thanks:

    Find the number of terms in this geometric series

    8/81 -4/27 + 2/9......-1 11/16 ( thats meant to be -1 and 11/16)

    You cant use logs this time so how do you do it. I just can't thinK!
    The common ratio is -3/2

    The kth term is 8/81 (-3/2)^(k-1)

    So you're looking to solve

    8/81 (-3/2)^(n-1) = -1 11/16 = - 27/16

    So

    (-3/2)^(n-1) = - (81 x 27)/(16 x 8) = -(3/2)^7

    So n-1 = 7

    So n = 8
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    So

    (-3/2)^(n-1) = - (81 x 27)/(16 x 8) = -(3/2)^7


    Got up to this bit. But how would you know that -(3/2)^7 without using logs or trial and error?
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    - (81 x 27)/(16 x 8) = - (9² x 3³)/ (4² x 2³)
    = - [ (3²)² x 3³ ] / [ (2²)² x 2³ ]
    = - [ 34 x 3³] / [24 x 2³]
    = - 37/27 = -(3/2)7
 
 
 
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