Final answer:
The next term in the sequence is -162, following the pattern where each term is multiplied by -3. The subsequent term should be 486, but it is not listed in the provided options; there might be a typo in the question. The correct answer is option A.
Step-by-step explanation:
The question asks us to complete the pattern for the next two terms in the sequence 2, -6, 18, -54. We can see that each term is multiplied by -3 to obtain the next term. Multiplying -54 by -3 gives us 162, and this pattern suggests that the term should be negative, so the next term is -162. Going one step further, multiplying -162 by -3 gives us 486, and again following the pattern, the term should be positive, hence the term is 486.
So, the complete pattern for the next two terms is: -162, 486.
However, since the options given do not include 486, we realize there might have been a typo or oversight in the options provided. The correct next two terms given the pattern should include -162 for the fifth term. For the sixth term, assuming no options available match the expected 486, we should select the closest match or inform the student of the discrepancy.