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Thread: GEMETRIC SEQUENCE task

  1. #1
    CEE
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    GEMETRIC SEQUENCE task

    Hello Everyone
    Please help with geometric sequence problem:
    A machine that produces an item that is being phased out will be disposed immediately after the last order of 900 parts is completed.The machine's monthly production is as follows : 300,210,147...How many months of production is needed in order to hire a part time worker.bear in mind that the machine's life has nearly come to an end where further maintenance costs are not necessary and too costly

    I have tried to solve it as follows; from geometric series given 210 dived by 300= 7/10 therefore the common difference is 7/10
    From geometric series sum formula S= a(r^n-1)/r-1, therefore 900=300(7/10^n-1)/ 0.7-1 which led me to 1/10=(7/10)^n. i can't solve it any further . please help where am getting it wrong
    Last edited by CEE; Jan 21st 2018 at 02:08 PM.
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  2. #2
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    Re: GEMETRIC SEQUENCE task

    1/10 = (7/10)^n

    n = log(1/10) / log(7/10) = ~6.45

    You were told in your previous thread that:
    if x^n = y, then n = log(y) / log(x)
    Already forgot?!

    n
    1.00: 300
    2.00: 210
    3.00: 147
    4.00: 103
    5.00: 072
    6.00: 050
    6.45: 018
    -----------
    total: 900
    Last edited by DenisB; Jan 21st 2018 at 04:34 PM.
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  3. #3
    CEE
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    Re: GEMETRIC SEQUENCE task

    Thank you for your help again, I didn't realise you introduced logs on the previous equation. however, I'm still little bit lost how you got the remaining sequence to get 900.
    on this sequence , I thought using a geometric progression formula,subtituting the values you should get a whole number or nearest to the whole number ? and i'm not sure how you getting nth items to have decimal of two zeros. sorry, i think i have lots to learn . thanks
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  4. #4
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    Re: GEMETRIC SEQUENCE task

    Sorry CEE; used .00 only to "keep columns at same width"!

    This would have been clearer (2nd column = term amount, 3rd column = "so far"):
    n
    1: 300 : 300
    2: 210 : 510
    3: 147 : 657
    4: 103 : 760
    5: 72 : 832
    6: 50 : 882
    7: 35 : 917

    Now you can "see" that 900 happens in between 882 and 917,
    or in between 6 and 7, thus the 6.45 solution.
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  5. #5
    CEE
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    Re: GEMETRIC SEQUENCE task

    Thanks a lot for your further explanation, apprieciate. NB , the question requires to calculate the total number of months, whole number. I'm not sure how can do that if 900 happens between 6 and 7? or missing something
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  6. #6
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    Re: GEMETRIC SEQUENCE task

    Round up or down, I guess:
    6: 50
    6.45: ?
    50 / 6 * 6.45 = 53.75 ; so 53 or 54, depending...
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  7. #7
    CEE
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    Re: GEMETRIC SEQUENCE task

    Quote Originally Posted by DenisB View Post
    Round up or down, I guess:
    6: 50
    6.45: ?
    50 / 6 * 6.45 = 53.75 ; so 53 or 54, depending...
    Thank you, i get how you came to the conclusion .though based on the question , i think there's something misleading
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  8. #8
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    Re: GEMETRIC SEQUENCE task

    Btw, most geometric don't have integer results.
    Integer results happen only when a, r and n are integers: understand?
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  9. #9
    CEE
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    Re: GEMETRIC SEQUENCE task

    Quote Originally Posted by DenisB View Post
    Btw, most geometric don't have integer results.
    Integer results happen only when a, r and n are integers: understand?
    Kind of, thank you.I need to do couple more to get the grasp of it
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