Pn = k*P(n-1) + h*P(n-2)
P2 = k*P1 + h*Po
= 9k + 8h
= 57
P3 = k*P2 + h*P1
= 57k + 9h
= 111
=> k = 1, h = 6
=> Pn = P(n-1) + 6*P(n-2)
Characteristic equation:
0= x^2 - x - 6 = (x-3)(x+2)
=> x = 3, -2
=> Pn = p*3^n + q*(-2)^n
Po = p + q = 8
P1 = 3p - 2q = 9
=> p = 5, q = 3
=> Pn = 5*3^n + 3*(-2)^n
=> P2 = 5*9 + 3*4 = 57
=> P3 = 5*27 - 3*8 = 111
=> P4 = 5*81 + 3*16 = 453
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