Question

Which of the following functions describes the sequence 4, -2, 1, -1/2?

A. f(1) = 4, f(n + 1) = –2f(n) for n ≥ 1
B. f(1) = 4, f(n + 1) = f(n) – 2 for n ≥ 1
C. f(1) = 4, f(n) = 12f(n + 1) for n > 1
D. f(1) = 4, f(n) = –12f(n – 1) for n > 1

Answer 1

The function that describes the sequence 4, -2, 1, -1/2 is option D. f(1) = 4, f(n) = –12f(n – 1) for n > 1.

Step-by-step explanation:

The function that describes the sequence 4, -2, 1, -1/2 is option D. f(1) = 4, f(n) = –12f(n – 1) for n > 1.

In this function, the first term is 4 and each subsequent term is obtained by multiplying the previous term by -12. For example, f(2) = -12 * f(1) = -12 * 4 = -48, f(3) = -12 * f(2) = -12 * -48 = 576, and so on.