The sequence \( \{x_n\} \) satisfies the relation
\[ \begin{array} &x_1 = -7, &x_2 = 0, &x_3 = 6, &x_{n+3} = 2 x_{n+2} + 5 x_{n+1} - 6 x_n, \end{array}\]
where \(n\) is a positive integer.
What is the value of \( x_6? \)

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The sequence \( \{x_n\} \) satisfies the relation
\[ \begin{array} &x_1 = 0, &x_2 = 1, &x_{n+2} + 2 x_{n+1} + x_n = 0 &(n = 1, 2, 3, \ldots). \end{array}\]
If \( x_n \) can be expressed as \[ a r^n + b n r^n, \] what is the value of \( \frac{b}{a}? \)

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