Find the general solution of the recurrence relation: an = an-1 + 2an-2 , with a0 = 2 and a1 = 7.
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Let us find the solution of the recurrence relation , with and . Let us solve the characteristic equation which is equivalent to , and hence by Vieta's formulas has the solutions and It follows that the solution of the equation is Since and , we have that and Therefore, and We conclude that