Which of the following sequences aₙ are solutions of the recurrence aₙ = 8aₙ₋₁ − 16aₙ₋₂? A. aₙ = 1 B. aₙ = 2ⁿ C. aₙ = 4ⁿ D. aₙ = n·4ⁿ E. aₙ = (−4)ⁿ
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Correct answer: C. C, D Only
Explanation
The characteristic equation r² − 8r + 16 = 0 has the double root 4, so the general solution is (c₁ + c₂n)·4ⁿ. 4ⁿ and n·4ⁿ fit; 1, 2ⁿ and (−4)ⁿ do not.
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