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What is the general form of the particular solution guaranteed to exist by Theorem $6$ of the linear nonhomogeneous recurrence relation $a_{n} = 6a_{n-1} - 12a_{n-2} + 8a_{n-3} + F (n)$ if

  1. $F (n) = n^{2}?$
  2. $F (n) = 2^{n}?$
  3. $F (n) = n2^{n}?$
  4. $F (n) = (-2)^{n}?$
  5. $F (n) = n^{2}2^{n}?$
  6. $F (n) = n^{3}(-2)^{n}?$
  7. $F (n) = 3?$
     
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