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Solve the difference equation?

Solve the difference equation yn+1=-0.9yn in terms of the initial value yo.

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On the contrary!

(-1)n(0.9)nyo is the same as (-0.9)ny0

Because -0.9 = (-1) x 0.9. Then you have to use the rule of exponents:

                                             (ab)n =anbn

Thus

                               (- 0.9)n = [(-1) x (0.9)]n = (-1)n (0.9)n

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