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Solve Finite Difference Equation

See attached file for full problem description with equation.

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Find analytically the solution of this difference equation with the given initial values:

Without computing the solution recursively, predict whether such a computation would be stable.

(Note: A numerical process is unstable if small errors made at one stage of the process are magnified in subsequent stages and seriously degrade the accuracy of the overall calculation.)
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Solution Preview

Please see the attached file.

Difference equation:
$$
x_{n+1} = -0.2 x_n + 0.99 x_n. eqno(1)
$$
Starting conditions:
$$
x_0 = 1, hskip 1cm x_1=0.9. eqno(2)
$$
This is a linear homogeneous equation with constant coefficients. Therefore its solutions are a linear combination of basic solutions of form
$$
B_n = cq^n,eqno(3)
$$
where $c$ and $q$ are constants.
Substituting the basic form (3) into equation ...

$2.19