Find the solution to the recurrence relation an = 3an−1+ 10an-2 with initial terms að = 7 and a₁ = 12. an =

Find the unique, closed form solution to this recurrence relation given the initial conditions: an = 6an-1-8an-2 for n ≥ 2, a₁ = 1, a₁ = 5

4. Find an explicit formula for the recurrence relation an= An-1+6an-2 ao= 5 aj = 0 %3D

Solve the recurrence relation, given: • ao = 3 • a₁ = 4 . • an = 5an-1-6an-2 Remember: • The theorem is an = c₁an-1 + c₂an-2. -b± √b² - 4ac 2a • The quadratic formula is O a O b Oc Od an = 5(4)" -2(3)" an = 5(2)"-2(3)" an = 5(2)"+2(3)" an = 5(3)" -2(3)"

Use the Frobenius method to solve: xy"-2y'+y=0. Find index r and recurrence relation. Compute the first 5 terms (a. -a4) using the recurrence relation for each solution and index r.

2. Find the solution of the recurrence relation an = 2an-1 +3.2".

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