In this investigation I have been asked to find out how many squares would be needed to make up a certain pattern accorting to its sequence.
In 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 sequential 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 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 aid of a diagram below;If we take sequence 3:2(1+3)+5=13 2(1 squares)2(3 squares) 1(5 squares)The Patterns I Have Noticied in Carrying Out the Previous MethodI have now carried out ny first investigation into the pattern and have seen a number of different patterns.Firstly I can see that the number of squares in each pattern is an odd number.Secondly I can see that the number of squares in the pattern can be found out by taking the odd numbers from 1