![]() ![]() Solve the system of equations to find the coefficients of the polynomial rule for the sequence.Form a system of equations, using the values from the original sequence, creating one more equation than the degree of the polynomial.Create the generic polynomial for that power for example, two rows would mean a degree-two, or quadratic, polynomial, with general form an 2 + bn + c.The number of rows below the original sequence row is equal to the power of the modelling polynomial.Continue until you get all the same values in a row, or until the last row has only one value. If the values in this row are not the same, then repeat the process, creating a third row of differences. If all of the subtractions give you the same value, you have shown the sequence to have a modelling polynomial of degree 1.You write the terms of the sequence in a row, and subtract consecutive terms, listing the "differences" below and between the pairs of terms, forming a second row.The method of common differences is a process for finding a polynomial rule for a sequence. In a number sequence, the order of the sequence is important, and depending on the sequence, it is possible for the same terms to appear multiple times. The numbers in the Fibonacci Sequence dont equate to a specific formula, however, the numbers tend to have certain relationships with each other. But what if a sequence is generated by a more complicated polynomial? Or you're tired and just not feeling very clever at the moment? How would you figure it out then? What is the method of common differences? An infinite sequence is a sequence that has an infinite number of terms and therefore never ends. Note that the first and third sequences above were generated by the polynomials n 2 and n 2 + 1, respectively. Eight 8 and eleven 11 are both fantastic numbers in our culture, and todays experience could be summarised thus: 6 + 2 + 3 11, which is absolutely beautiful. ![]()
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