Final answer:
The first three terms of the sequence with the explicit rule f(n) = 2-3(n-1) are 2, -1, and -4.
Step-by-step explanation:
You are asked to find the first three terms of the sequence with the explicit rule f(n) = 2-3(n-1). To do this, simply substitute the values of n (1, 2, and 3) into the formula and calculate the resulting terms.
- For n = 1: f(1) = 2 - 3(1 - 1) = 2 - 3(0) = 2 - 0 = 2
- For n = 2: f(2) = 2 - 3(2 - 1) = 2 - 3(1) = 2 - 3 = -1
- For n = 3: f(3) = 2 - 3(3 - 1) = 2 - 3(2) = 2 - 6 = -4
Therefore, the first three terms of the sequence are 2,−1,−4. The sequence follows a pattern of decreasing by 3 with each term. This pattern is consistent with the explicit rule f(n) = 2-3(n-1).