Question

Find the solution to the following lhcc recurrence:

an=22an−1−117an−2 for n≥3 with initial conditions
a0=−18,a1=−226.
an=

Answer 1

To find the solution to the given LHCC recurrence, use the characteristic equation method. The general solution is an = A(13)^n + B(9)^n.

Step-by-step explanation:

To find the solution to the given LHCC recurrence, we can use the characteristic equation method. The characteristic equation is found by setting the expression inside the recurrence bracket equal to zero.

So, the characteristic equation for the given recurrence is r^2 - 22r + 117 = 0.

By solving this quadratic equation, we find that r = 13 and r = 9.

Therefore, the general solution to the recurrence is:

an = A(13)^n + B(9)^n,

where A and B are constants determined using the initial conditions.