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October 20th, 2008, 08:04 AM
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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] |
October 20th, 2008, 08:11 AM
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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? |
October 20th, 2008, 08:16 AM
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Quote:
Originally Posted by batman  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! |
October 20th, 2008, 08:20 AM
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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. | | The following users thank batman for this useful post: | |  | | Thread Tools | | | | Display Modes |  Linear Mode | 
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