SOLUTION: Consider the sequence:6;6;2;-6;-18 Determine an expression for the nth term,Tn

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Question 674615: Consider the sequence:6;6;2;-6;-18


Determine an expression for the nth term,Tn
Answer by solver91311(24713) About Me  (Show Source):
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Use the method of common differences: 



      6     6     2    -6   -18
       \   / \   / \   / \   / 
         0    -4    -8   -12 
          \   / \   / \   /
           -4    -4    -4


The differences become common at the 2nd level down, hence the desired model for the nth term is going to be a 2nd degree polynomial.



The value of the term when n = 1 is 6, so:



Which is to say:



Using similar logic, we develop:



and



Solve the 3X3 system to find the values of the coefficients for

John

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