Final answer:
The recursive formula for the sequence 4, 2, 1, 1/2 is a1 = 4 and an = (1/2) * an-1. The next three terms are 1/4, 1/8, and 1/16.
Step-by-step explanation:
The given sequence is 4, 2, 1, 1/2. To find the recursive formula for this sequence, we look for a pattern or rule that relates each term to the previous term. In this case, we can observe that each term is half of the previous term. So, the recursive formula for this sequence is:
a1 = 4
an = (1/2) * an-1
To find the next three terms, we can substitute the values of n into the recursive formula:
a5 = (1/2) * a4 = (1/2) * (1/2) = 1/4
a6 = (1/2) * a5 = (1/2) * (1/4) = 1/8
a7 = (1/2) * a6 = (1/2) * (1/8) = 1/16