Question

Which of the following functions describes the sequence 4, –2, 1, –12, 14, . . .?

Answer 1

D. f(1) = 4, f(n) = –1/2f(n – 1) for n > 1

Explanation:

We assume your sequence is supposed to be ...

4, -2, 1, -1/2, 1/4, ...

This has no common difference, but it has a common ratio of -1/2. That is, the first term is 4, and each successive term is -1/2 times the previous one. The function is described by the recursive formula ...

f(1) = 4;

f(n) = -1/2·f(n-1)