Answer:
Pn = A * e ^ (4 * n) + B * e ^ (- 2 * n)
Step-by-step explanation:
We have the following:
Pn = 2 * P_n-1 + 8P_n-2
the characteristic equation is as follows:
L ^ 2 - 2 * L - 8 = 0
Which is equal to:
Ā L ^ 2 - 4 * L + 2 * L - 8 = 0
we factor:
L * (L - 4) + 2 * (L - 4) = 0
From here we can deduce that:
L = -2
L = 4
Thus:
Pn = A * e ^ (4 * n) + B * e ^ (- 2 * n)
