Intermediate Discrete Mathematics & Math
Q71 / 100

What technique is typically used to solve a linear homogeneous recurrence relation like a_n = 5a_{n-1} - 6a_{n-2}?

Correct! Well done.

Incorrect.

The correct answer is B) Form the characteristic equation x² = 5x - 6, solve for its roots, and write the general solution as a linear combination of those roots raised to the n-th power

B

Correct Answer

Form the characteristic equation x² = 5x - 6, solve for its roots, and write the general solution as a linear combination of those roots raised to the n-th power

Explanation

For a_n = 5a_{n-1} - 6a_{n-2}, the characteristic equation x² - 5x + 6 = 0 factors as (x-2)(x-3) = 0, giving roots 2 and 3. The general solution is a_n = A·2ⁿ + B·3ⁿ, with A and B determined by initial conditions.

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71/100