Solve the recurrence relation an = 5an-1 - 6an-2, with initial conditi | Discrete Structures 2078

Discrete Structures20785 marksNumerical: solving recurrence relationSolving Recurrence Relations

Solve the recurrence relation $a_n = 5a_{n-1} - 6a_{n-2}$ , with initial conditions $a_0 = 1$ , $a_1 = 4$ . [5]

Solve the recurrence relation $a_n = 5a_{n-1} - 6a_{n-2}$, with initial conditions $a_0 = 1$, $a_1 = 4$. [5]

$an = 5a{n-1} - 6a{n-2}, \quad a0 = 1,\ a1 = 4$ Characteristic equation. Assume $an = r^n$ : $r^2 = 5r - 6 \implies r^2 - 5r + 6 = 0$ Roots: $(r-2)(r-3) = 0 \implies r1 = 2,\ r2 = 3$ Distinct roots, so the general solution is: $an = \alpha1 \cdot 2^n + \alpha2 \cdot 3^n$ Apply initial cond...

$$an = 5a{n-1} - 6a{n-2}, \quad a0 = 1,\ a1 = 4$$ Characteristic equation. Assume $an = r^n$: $$r^2 = 5r - 6 \implies r^2 - 5r + 6 = 0$$ Roots: $$(r-2)(r-3) = 0 \implies r1 = 2,\ r2 = 3$$ Distinct roots, so the general solution is: $$an = \alpha1 \cdot 2^n + \alpha2 \cdot 3^n$$ Apply initial cond...

← PreviousAll questions Next question →

Up nextProve that if n is positive integer, then n is odd if and only if 5n + 6 is odd.

Solve the recurrence relation an = 5an-1 - 6an-2, with initial conditions a0 = 1, a1 = 4.