Solve the recurrence relation an = 5an-1 - 6an-2, with initial conditi | Discrete Structures 2075

Discrete Structures20755 marksNumerical: solving recurrence relationSolving Recurrence Relations

Solve the recurrence relation $a_n = 5a_{n-1} - 6a_{n-2}$ , with initial conditions $a_1 = 1$ and $a_2 = 2$ . [5]

Solve the recurrence relation $a_n = 5a_{n-1} - 6a_{n-2}$, with initial conditions $a_1 = 1$ and $a_2 = 2$. [5]

Recurrence: $an = 5a{n-1} - 6a{n-2}$ - Initial conditions: $a1 = 1$ , $a2 = 2$ This is a linear homogeneous recurrence of degree 2 with constant coefficients. --- Substitute $an = r^n$ : $r^2 = 5r - 6 \implies r^2 - 5r + 6 = 0$ Factor: $(r-2)(r-3) = 0 \implies r1 = 2,\ r2 = 3$ Distinct roots,...

Recurrence: $an = 5a{n-1} - 6a{n-2}$ - Initial conditions: $a1 = 1$, $a2 = 2$ This is a linear homogeneous recurrence of degree 2 with constant coefficients. --- Substitute $an = r^n$: $$r^2 = 5r - 6 \implies r^2 - 5r + 6 = 0$$ Factor: $$(r-2)(r-3) = 0 \implies r1 = 2,\ r2 = 3$$ Distinct roots,...

Solve the recurrence relation an = 5an-1 - 6an-2, with initial conditions a1 = 1 and a2 = 2.