Final answer:
The first 4 terms of the sequence, calculated using two different definitions, are 64, 32, 16, and 8. These terms are consistent with a sequence where each term is half the previous term.
Step-by-step explanation:
The question is asking to list the first 4 terms of a sequence defined by two different expressions. Let's calculate the terms using both definitions.
Definition One states that f1=64 and fn= 1/2 * f(n-1) for n ≥ 2. This definition describes a sequence where each term is half of the previous term. Starting with f1:
-
- f1 = 64
-
- f2 = 1/2 * f1 = 1/2 * 64 = 32
-
- f3 = 1/2 * f2 = 1/2 * 32 = 16
-
- f4 = 1/2 * f3 = 1/2 * 16 = 8
Definition Two proposes fn=64 * (n-1)^1/2 for n ≥ 1. However, the second definition seems to have a typo, as raising (n-1) to the 1/2 power (square root) would not result in a sequence where each term is half the previous one. Therefore, it's likely that '1/2' is supposed to indicate the exponent of the sequence rather than a square root. Assuming the correct expression is fn=64 * (1/2)^(n-1), we would get the same sequence:
-
- f1 = 64 * (1/2)^(1-1) = 64 * 1 = 64
-
- f2 = 64 * (1/2)^(2-1) = 64 * 1/2 = 32
-
- f3 = 64 * (1/2)^(3-1) = 64 * 1/4 = 16
-
- f4 = 64 * (1/2)^(4-1) = 64 * 1/8 = 8