Final answer:
The sequence 3, -3, -9, -15 decreases by 6 each time and the correct rule is 'start with 3 and add -6 repeatedly'. Therefore, the correct answer is option A. start with 3 and add -6 repeatedly.
Step-by-step explanation:
The student is asking for a rule that can be applied to generate the sequence 3, -3, -9, -15. This sequence is decreasing by 6 each time. We can determine the correct rule by evaluating how the sequence progresses from one term to the next. Clearly, each term after the first is obtained by subtracting 6 from the previous term, which can be restated as adding -6.
The correct rule for this sequence is Option A: start with 3 and add -6 repeatedly. This rule reflects the consistent change between terms in the sequence.
Examples to demonstrate:
First term: 3
Second term: 3 + (-6) = -3
Third term: -3 + (-6) = -9
Fourth term: -9 + (-6) = -15