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Using the Difference Method to Find an Equation to Establish the Number of Squares in a 3D Version of the Pattern  

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Using the Difference Method to Find an Equation to Establish the Number of Squares in a 3D Version of the Pattern Pos.in seq. 0 1 2 3 4 5 No.of squar. -1 1 7 25 63 129 1st differ. 2 6 18 38 66 2nd differ. 4 12 20 28 36 3rd differ. 8 8 8 8 So therefore we get the equation; anƒ + bn2 + cn + d We already know the values of 'n' (position in sequence) in the equation so now we have to find out the values of a, b, c, and d. If n = 0 then d = -1 and if n = 1 then d = 1 I can now get rid of d from the equation to make it easier to find the rest of the values. I will will take n = 2 to do this in the following way: 1st calculation _ 8a + 4b...

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