Q4Discrete Mathematics Structure

Question

Solve the recurrence relation : a_r = 2a_{r-1} - a_{r-2}, r ≥ 2, with a_0 = 1, a_1 = 2.

Answer 1

Characteristic equation: $r^{2} - 2 r + 1 = 0 ⟹ (r - 1)^{2} = 0$ . Double root $r = 1, 1$ .

General solution: $a_{r} = (C_{1} + C_{2} r) (1)^{r} = C_{1} + C_{2} r$ .

Apply initial conditions:

Particular solution: $a_{r} = r + 1$ .

Question