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Math Help - geometric Sequence

  1. #1
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    geometric Sequence


    (b) Consider the following geometric sequence.
    400
    ,
    320
    ,
    256
    ,
    204
    .8,
    ...
    (i)
    Write down a recurrence system that describes this sequence.
    (Denote the sequence by
    xn,and itsfirsttermby x1.)
    [
    2]
    (ii) Find a closed form for this sequence.
    [
    2]
    (iii) Use the closed form from part (b)(ii) to find the tenth term of the
    sequence, giving your answer correct to four decimal places.
    [
    2]
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  2. #2
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    note 320/400=0.8 (=256/320=...). You thus find x_n = 0.8 x_(n-1), the closed form is then given by x_n = 400*(0.8)^(n-1).
    Can you do the other exercise yourself now?
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  3. #3
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    Quote Originally Posted by batman View Post
    note 320/400=0.8 (=256/320=...). You thus find x_n = 0.8 x_(n-1), the closed form is then given by x_n = 400*(0.8)^(n-1).
    Can you do the other exercise yourself now?
    Im not sure i understand the 320/400 part but am not sure of the formula you have given.

    PLease help, thankyou so far!
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  4. #4
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    You have the sequence 400, 320, 256, 204.8. Now you see that the next one is the previous one times 0.8 as 320=400*0.8, 256=320*0.8 and 204.8=256*0.8. More generally you have x_n = 0.8*x_(n-1) with x_1=400.
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