![]() ![]() Note that we can also solve a system of 3 linear equations in 3 variables by using 3 distinct points in the sequence. This means that our general term (formula) for this quadratic sequence is: Since -3 = b + c and b = -4, we find c = 1. Now, we can easily solve this system of equations with elimination by subtracting the equations: ![]() Next, we look at the first and second terms of the sequence. This tells us that we have a quadratic sequence.įirst, we divide this second difference by 2 to get 4 /2 = 2. We can see that the second differences are all the same (they have a value of 4). Rence -1 1 2 7 6 4 17 10 4 31 14 4 Table of terms, first differences, and First, we create a table of first and second differences: Term So, what is a quadratic sequence? A quadratic sequence is an ordered set with constant second differences (the first differences increase by the same value each time). Some of them are arithmetic or geometric, and some are linear or quadratic. When working with sequences of numbers, it helps to be able to recognize patterns. See in particular p. 81: "A breeder is any pattern which grows quadratically by creating a steady stream of copies of a second object, each of which creates a stream of a third." ^ Griffeath, David Hickerson, Dean (2003), "A two-dimensional cellular automaton crystal with irrational density", New constructions in cellular automata, St.(ed.), Algorithms and Theory of Computation Handbook, Boca Raton, Florida: CRC, pp. 3-1–3-25, MR 1797171. ![]()
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