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Math Help - Need help with finding equal for geometric series

  1. #1
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    Exclamation Need help with finding equal for geometric series

    In 2004, US natural gas consumption was 646.7 billion cubic meters. Asian consumption was 367.7 billion cubic meters. During the previous decade, US consumption increased by 0.6% a year, while Asian consumption grew by 7.9% a year. Assume these rates continue into the future.

    a) Give the first four terms of the sequence, an, giving US consumption of natural gas n years after 2003.

    b) Give the first four terms of a similar sequence b_n showing Asian gas consumption.



    I need some clarification. What do they mean n years after 2003. I want to put it in the formula (a_n) * (r)^(n-1).
    a_n is initial
    r is rate

    So for a problem such as a), to find the a_n of 2003 do we multiply 646.7 by 0.006 to get 642.81?

    So a formula for part a) should be: 642.81(1.006)^n-1?
    Same thing with part b)

    Please correct me if I am wrong. Thank you.
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  2. #2
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    Quote Originally Posted by florx View Post

    I need some clarification. What do they mean n years after 2003. I want to put it in the formula (a_n) * (r)^(n-1).
    a_n is initial
    r is rate
    This sounds good. The year 2004 should be n=1 In this case.


    Quote Originally Posted by florx View Post



    So for a problem such as a), to find the a_n of 2003 do we multiply 646.7 by 0.006 to get 642.81?
    Is this an increase?


    Quote Originally Posted by florx View Post

    So a formula for part a) should be: 642.81(1.006)^n-1?
    Same thing with part b)
    This is better, what do you get?
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  3. #3
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    Quote Originally Posted by pickslides View Post




    Is this an increase?




    This is better, what do you get?

    It is a decrease because the problem said that "During the previous decade, US consumption increased by 0.6% a year" so the US 2003's natural consumption should be less than 2004.

    So is that formula I wrote correct?
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  4. #4
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    Quote Originally Posted by florx View Post
    giving US consumption of natural gas n years after 2003.
    I understand "after 2003" to be 2004, 2005, 2006 and 2007.

    Now use 646.7(1.006)^{n-1} where 2004 \implies n=1
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  5. #5
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    Oh thank you so much for helping me. I misread the problem and thought they wanted the consumption of 2003 as a_n.
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