Find the solution of the recurrence relation: xn=3xn-1 + 1, where, x0=4
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Let us find the solution of the recurrence relation: , where
For this firstly, let us solve the characteristic equation of the homogeneous equation :
or It follows that the particular solution of the equation is , where and hence The solution of the recurrence relation:
is Taking into account that we conclude that , and thus Consequently,