Problem 3

Let Zn denote the nth term in a sequence Z, and suppose Zn is defined by equation Zn = .5(Zn-1)² - 6. If Z1 = 2, what is the 5th term of the sequence?

(A) -2
(B) 2
(C) 6.5
(D) 355
(E) 728

Let's
apply the formula to generate successive terms after the first. The
formula tells you that in order to get the next term, you take the
previous term, square it and multiply by .5, and then subtract 6.

Z1 = 2
Z2 = .5(2)² - 6 = -4
Z3 = .5(-4)² - 6 = 2
Z4 = .5(2)² - 6 = -4
Z5 = .5(-4)² - 6 = 2

The fifth term of the sequence is Z5, so the correct answer is B.