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Advanced Arithmetic

Hi I was wondering if someone can check to see if this question is correct that I have attempted I am pretty confident this is correct though. Many Thanks. 2.A particle oscillates in a straight line. It starts at A. It moves 10m to point B. It then reverses and returns 7.5m. It continues to change direction and travel 75% of the previous leg. By the time it stops how far does it travel and where would it finish? D = 10(0.75)^0 + 10(0.75)^1 + 10(0.75)^2 +.... P = 10(-0.75)^0 + 10(-0.75)^1 + 10(-0.75)^2 + ...
S = (a_1) / (1 - R) where R is the common ratio.

So

D = 10 / (1 - 0.75) = 10 / 0.25 = 40m

and

P = 10 / (1 - (-.75)) = 10 / 1.75 = 40/7 = 5.714m
Absolutely correct. This is a geometric progression with r=0.75 for distance travelled and r= -0.75 for location of the particle.

Well done. Peace.

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