2D & 3D Sequences.

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2D & 3D Sequences Plan of InvestigationIn this experiment I am going to require the following:A calculatorA pencil A penVariety of sources of informationPaperRulerIn this investigation I have been asked to find out how many squares would be needed to make up a certain pattern according to its sequence. The pattern is shown on the front page. In this investigation I hope to find a formula which could be used to find out the number of squares needed to build the pattern at any sequencial position.Firstly I will break the problem down into simple steps to begin with and go into more detail to explain my solutions. I will illustrate fully any methods I should use and explain how I applied them to this certain problem. I will firstly carry out this
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experiment on a 2D pattern and then extend my investigation to 3D. The Number of Squares in Each SequenceI have achieved the following information by drawing out the pattern and extending upon it.Seq. no. 1 2 3 4 5 6 7 8No. Of cubes 1 5 13 25 41 61 85 113I am going to use this next method to see if I can work out some sort of pattern:Sequence Calculations Answer1 =1 12 2(1)+3 53 2(1+3)+5 134 2(1+3+5)+7 255 2(1+3+5+7)+9 416 2(1+3+5+7+9)+11 617 2(1+3+5+7+9+11)+13 858 2(1+3+5+7+9+11+13)+15 1139 2(1+3+5+7+9+11+13+15) +17 145 What I am doing above is shown with the ...

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