Final answer:
The sequence defined by f(n) = f(n - 1) - 7, with f(1) = 42, yields the first five terms as 42, 35, 28, 21, and 14. The sequence has a domain of positive integers, no intercepts, a decreasing interval from the start, a maximum of 42, and a minimum within the first five terms as 14, while being a discrete sequence with also an undefined overall minimum, since it decreases indefinitely.
Step-by-step explanation:
The sequence is defined by the recursive rule: f(n) = f(n - 1) - 7, with the initial condition f(1) = 42. Let's determine the first five terms of the sequence.
- f(1) = 42 (given)
- f(2) = f(1) - 7 = 42 - 7 = 35
- f(3) = f(2) - 7 = 35 - 7 = 28
- f(4) = f(3) - 7 = 28 - 7 = 21
- f(5) = f(4) - 7 = 21 - 7 = 14
Therefore, the first five terms of the sequence are 42, 35, 28, 21, and 14.
The domain of this sequence is the set of all positive integers since we are looking at the sequence term by term starting from n=1.
There are no intercepts because the sequence is not a continuous function but rather a series of discrete points.
The range of the first five terms is {42, 35, 28, 21, 14}.
Interval(s) of increase: This sequence does not increase; it only decreases as n increases.
Maximum: The maximum value is the first term, which is 42.
Interval(s) of decrease: The whole sequence is decreasing; thus, it decreases from the first term onwards.
Minimum: The minimum within the first five terms is the last term, which is 14. However, the minimum value of the entire sequence is not defined as the sequence is infinitely decreasing.
This is a discrete sequence since it is defined only for integer values of n, and there are clear jumps from one term to the next with nothing in between.