Practice Summary And References (19.2.7) - Lecture -39: Solving Linear Non- Homogeneous Recurrence Equations

Practice: Summary and References

Lesson 19.2.7Lecture -39: Solving Linear Non- Homogeneous Recurrence Equations

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6 sample questions

Question 1.
What is a linear non-homogeneous recurrence equation?
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Think about how these terms are structured.
Question 2.
Define the associated homogeneous recurrence relation.
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What does it leave you with?
3Question 3.
What is the general form of a linear non-homogeneous recurrence equation?
- a(n) = c_1*a(n-1) + c_2*a(n-2) + F(n)
- a(n) = F(n)
- a(n) = 2*a(n-1)
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Look for the version that includes both previous terms and F(n).
4Question 4.
True or False: A homogeneous equation does not include any function F(n).
- True
- False
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Consider the definitions we've discussed.
Question 5.
Given the recurrence relation a(n) = 2*a(n-1) + n^2, derive the general solution.
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Focus on the polynomial degree and ensure your guesses are structured correctly.
Question 6.
If F(n) includes an exponential function not part of the characteristic roots, how would you derive the particular solution?
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What structures might connect well without duplicating characteristics?

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