8. Consider the nonhomogeneous linear recurrence relation a, =За, -1 + 2"(a) Show that a,-2n+1 is a solution of this recurrence relation.(b) Find all the solutions of this recurrence relation.(c) Find the solution with ao = 1.

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Answered: Consider the nonhomogeneous linear…

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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Solve the recurrence relation an = -8a, 1- 16a, 2; ao = 1, a1=2 Answer:
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DO NOT COPY FROM OTHER WEBSITES Q. Solve the recurrence relation T(n) =T(n-4) + n2^n
13. Solve the recurrence relation. Given:a0=3 a1= 6 an= 6a n-1 + 7a n-2 Show your work in the space provided. a. Find c1 and c2 an= (6)a n-1 + (7)a n-2 c1= c2= b. Substitute c1 and c2 into the following equation: r^2- c1r - c2= 0 show your work here: c. Identify a, b, and c in the quadratic equation. a= b= c= d. Use the quadratic formula to find the two roots. Here is the quadratic formula: -b + Vb^2- 4ac/2a Show your work here: e. Substitute two roots, r1 and r2 into the equation an= a1r1^n+ a2r2^n Show your work here: f. Now substitute to find two equations, a0 and a1 Remember to use the equation you found from step e. show your work here: a0= 3 =a1= 6 = g. Add the two equations together find a1 and a2 a1= a2= h. What is the solution to the recurrence relations? an= i. Find the 10" term of the sequence, using the solution to the recurrence relation you just found. Show your work here: a10=
5. Solve the recurrence relation an = 3an-1- 2an-2 with initial conditions ao = a, a1 = b. Here a and b are constants. Зап-1 — 2ап-2 %3D
Solve the following recurrence relations, i.e., find closed-form expressions for an. For each case, state which technique you are using and provide detailed steps for your solutions. (a) an = an-1, ao = 4 (b) an 3an-1-1, a = 10 2an-1+1,00 = 0 (c) an (d) an = 2an-1 + 2an-2, ao = 3, a₁ = 3
solve this recurrence relations with the given initial conditions. Use an Iterative approach an = 2an-1 - 3, a0 =1
Consider the nonhomogeneous linear recurrence relation a, = 3a,-1 + 2" %3D (a) Show that an -2"+1 is a solution of this recurrence relation. (b) Find all the solutions of this recurrence relation. (c) Find the solution with ao = 1.
Solve the linear recurrence relation given by xn=4xn-1 + 12xn-2 with x1= 18 and x2 = 12
Find the solution to the recurrence relation by using an iterative approach. The recurrence relation a, = -5a, - 1 with the initial condition ao = 3 a. The solution for the recurrence relation is an = -5a, - 1 = (-5)?a,-2 = - .. = (-5)"an - n = (-5)"ao = 3 - (-5)" O b. The solution for the recurrence relation is an = -5an - 1 = 5an - 2 =- · = 5a, - n = 5a0 = 5(3) = 15 %3D O c. The solution for the recurrence relation is an = -5a, - 1 = (-5)²a, - 2 = · . = (-5)"a, - n = (-5)°ao = 1.3 = 3 %3D d. The solution for the recurrence relation is an = -5a, - 1 = -5an -2 = - -5a, - = -5a0 = -5(3) = 15
What is the solution to the recurrence relation: Tn=5nTn-1+6 with T0=3?

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Consider the nonhomogeneous linear recurrence relation a, = 3a,-1+2" (a) Show that a, = -2"+1 is a solution of this recurrence relation. (b) Find all the solutions of this recurrence relation. (c) Find the solution with ao = 1.