Consider the recurrence relation ak = 6ak-1 - 9ak-2 with initial conditions a0 = 0 and a1 = 2. Which of the following is an explicit solution to this recurrence relation, provided the constants A and B are chosen correctly?

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Q. Consider the recurrence relation ak = 6ak-1 - 9ak-2 with initial conditions a0 = 0 and a1 = 2. Which of the following is an explicit solution to this recurrence relation, provided the constants A and B are chosen correctly?

(A) an = A3n + B3n
(B) an = A3n + B(-3)n
(C) an = A3n + nB3n
(D) an = A(-3)n + nB(- 3)n

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✅ Correct Answer: (C) an = A3n + nB3n

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