You may want to review Solving Simulataneous Linear Equations with Gaussian Elimination before working these problems.

Find an explicit formula F(n) for each of the following recurrences. Find the characteristic equation; the roots of that equation; and appropriate values for the constant coefficients.

1. a_n = 3a_n-1, a₀ = 1

2. a_n = 2a_n-1 + 3a_n-2, a₀ = a₁ = 1

3. a_n = -3a_n-1 + 4a_n-2, a₀ = a₁ = 2

4. a_n = 4a_n-2, a₁ = 1, a₂ = 3, a₃ = 4

5. a_n = -3a_n-1 + a_n-2 + 3a_n-3, a₀ = a₁ = a₂ = 1

  Note: Make sure you review section 5.2 of Rosen before solving the last two problems.

6. a_n = 4a_n-1 - 4a_n-2, n > 1, a₂ = 3, a₃ = 5.

7. a_n = 6a_n-1 - 12a_n-2 + 8a_n-3, a₁ = 7, a₂ = 28, a₃ = 56
 

Solutions
 

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This page last modified 12/3/1999.
Copyleft 1999 Brian K. Hare.