A student programs a computer to draw a series of straight lines with each line beginning at the end of the previous line and at right angles to it. The first line is 4 mm long. Each subsequent line is 25% longer than the previous one, so that a spiral shape is formed. What is the length, in mm, of the eighth straight line drawn by the program? Express your answer to the nearest tenth of a mm.
http://picascii.com/upload/1355812815-V5…
(I made this quick in paint to show you the shape, nothing is to scale and the angles are not correct)
MY question is, is there a way to find out what the eighth term is besides finding out the length of the next line until you get to the eighth one?
http://picascii.com/upload/1355812815-V5…
(I made this quick in paint to show you the shape, nothing is to scale and the angles are not correct)
MY question is, is there a way to find out what the eighth term is besides finding out the length of the next line until you get to the eighth one?
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There is, the length of the n'th line is 4*(1.25)^(n-1) so the first line has length 4mm of course and the second 5, third 5*1.25 etc. The 8th line has length 4*(1.25)^7 = 19.1mm
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Yes. This is the same as figuring compound interest with the principal eyual to 4 and the interest equal to 25% per year or month or any period you wish.
calculate the total for eight periods and you get, 23.812.
calculate the total for eight periods and you get, 23.812.