Final answer:
The next term in the geometric sequence (4/9), -(4/3), 4, is -12, calculated by multiplying the third term 4 by the common ratio -3. The options provided in the question do not include this answer.
Step-by-step explanation:
The recursive formula for a geometric sequence can be defined as an = an-1 × r, where an is the nth term, an-1 is the previous term, and r is the common ratio of the sequence. To find the recursive formula for the given geometric sequence (4/9), -(4/3), 4, ___, we first need to find the common ratio (r). This can be done by dividing the second term by the first term.
So, r = -(4/3) / (4/9) = -3. To find the next term, we will multiply the third term by our common ratio:
a4 = 4 × -3 = -12. Thus, the next term in the sequence is -12, which is not listed in the multiple choice options provided with the question. The correct full sequence up to the fourth term is: (4/9), -(4/3), 4, -12.