<PRE><B>Question 1114820</B>
4, 6, 11
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we know we have an n^2 term
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general form of quadratic sequence is
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An^2 +Bn +C 
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using the sequence elements, we have 3 equations in 3 unknowns
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A + B + C = 4
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4A +2B +C = 6
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9A +3B +C = 11
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solve using a 3 by 3 linear system method or solver
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A = 1.5, B = -2.5, C = 5
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X(n) = 1.5n^2 -2.5n +5
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a) x(4) = 1.5 * 4^2 -2.5 * 4 +5 = 19
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b) 1.5n^2 -2.5n +5 = 81
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1.5n^2 -2.5n -76 = 0
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use quadratic formula to solve for n 
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n = (-(-2.5) +square root((-2.5)^2 -4 * 1.5 * (-76)) / (2*1.5) = 8
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n = (-(-2.5) -square root((-2.5)^2 -4 * 1.5 * (-76)) / (2*1.5) = -6.3333
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we reject the negative value for n
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n = 8
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