If a0 = 1, a1 = 3 and (aN)^2 - aN-1aN+1 = (-1)^n, determine a4 showing all of your work.

n = 1:
(a(1))^2 - a(0) a(2) = (-1)^1 ==> 3^2 - 1 * a(2) = -1 ==> a(2) = 10.

n = 2:
(a(2))^2 - a(1) a(3) = (-1)^2 ==> 10^2 - 3 * a(3) = 1 ==> a(3) = 33.

n = 3:
(a(3))^2 - a(2) a(4) = (-1)^3 ==> 33^2 - 10 * a(3) = -1 ==> a(4) = 109.

I hope this helps!