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2D and 3D Sequences Project Plan of Investigation
In this experiment I am going to require the following:
A calculator
A pencil
A pen
Variety of sources of information
Paper
Ruler
In 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. ... I will firstly carry out this experiment on
a 2D pattern and then extend my investigation to 3D. ...
If a = 2 then c = 1 and a + b = 0 If
2 is equal to b- then b = -2
I will now work out the equation using the information I have obtained
through using the difference method:
1) 2(n -1) (n - 1) + 2n - 1
2) 2(n2 - 2n + 1) + 2n - 1
3) 2n2 - 4n + 2 + 2n - 1
4) 2n2 - 2n + 1
Therefore my final equation is:
2n2 - 2n + 1
Proving My Equation and Using it to Find the Number
of Squares in Higher Sequences
I will now prove my equation by applying it to a number of sequences
and higher sequences I have not yet explored. ... The method in which
Iused to look for any patterns in the sequences. ...
Sequence 10:
N = 10
_(10ƒ) - 2(102) + 2Y(10) - 1 =
13335 - 200 + 26Y - 1 =
1159
Sequence 15:
N = 15
_(15ƒ) - 2(152) + 2Y(15) - 1 =
4500 - 450 + 40 - 1 =
4089
This equation has correctly given me the number of squares in each
sequence which again proves it can be applied to any of the 3D sequences
to give the correct answer. ...
Firstly I have deciferred that the equation used in the 2D pattern
was a quadratic.
Approximate Word count = 1330
Approximate Pages = 5.3
(250 words per page double spaced)
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