Determine values of the constants A and B such that an = An + B is a solution of recurrence relation an = 2an−1 + n + 5. Hence, find the solution of this recurrence relation with a0 = 4.
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Let us determine values of the constants and such that is a particular solution of the recurrence relation
It follows that
We conclude that is a paticular solution of the recurrence relation.
Further, let us find the general solution of this recurrence relation with
It follows that the characteristic equation has the solution and hence the general solution is of the form Since we conclude that
Consequently, the general solution of this recurrence relation with is