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  1. Determine values of the constants $A$ and $B$ such that $a_{n} = A{n} + B$ is a solution of recurrence relation $a_{n} = 2a_{n-1} + n + 5.$
  2. Use Theorem $5$ to find all solutions of this recurrence relation.
  3. Find the solution of this recurrence relation with $a_{0} = 4.$
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