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Solve the recurrence relation. Given: • a, = 9, • az = 10, a, = 8a,-1- 12a,-2 Remember: The theorem is an = cịan-1+ C2an-2. -6+ v – 4ac The quadratic formula is 2a -2(6)" + 11(2)" a an a, = -2(6)" + 10(2)" a, = -(9)" + 11(2)" an = -(8)" + 2(11)"

Solve the recurrence relation. Given: • a, = 9, • az = 10, a, = 8a,-1- 12a,-2 Remember: The theorem is an = cịan-1+ C2an-2. -6+ v – 4ac The quadratic formula is 2a -2(6)" + 11(2)" a an a, = -2(6)" + 10(2)" a, = -(9)" + 11(2)" an = -(8)" + 2(11)"

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The problem asks to solve the recurrence relation with the following details: ### Given: - Initial conditions: \( a_0 = 9 \) \( a_1 = 10 \) - Recurrence relation: \( a_n = 8a_{n-1} - 12a_{n-2} \) ### Remember: - The theorem: \( a_n = c_1a_{n-1} + c_2a_{n-2} \) - Quadratic formula for characteristic equation roots: \( \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) ### Options for the solution: - (a) \( a_n = -2(6)^n + 11(2)^n \) - (b) \( a_n = -2(6)^n + 10(2)^n \) - (c) \( a_n = -(9)^n + 11(2)^n \) - (d) \( a_n = -(8)^n + 2(11)^n \) This is a typical problem for solving linear homogeneous recurrence relations using characteristic equations.
Transcribed Image Text:The problem asks to solve the recurrence relation with the following details: ### Given: - Initial conditions: \( a_0 = 9 \) \( a_1 = 10 \) - Recurrence relation: \( a_n = 8a_{n-1} - 12a_{n-2} \) ### Remember: - The theorem: \( a_n = c_1a_{n-1} + c_2a_{n-2} \) - Quadratic formula for characteristic equation roots: \( \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) ### Options for the solution: - (a) \( a_n = -2(6)^n + 11(2)^n \) - (b) \( a_n = -2(6)^n + 10(2)^n \) - (c) \( a_n = -(9)^n + 11(2)^n \) - (d) \( a_n = -(8)^n + 2(11)^n \) This is a typical problem for solving linear homogeneous recurrence relations using characteristic equations.
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