a sequence is defined by the recursive formula (f(n + 1)=1.5f(n)). which sequence could be generated using…

Explanation:

Step1: Identify the common - ratio property

The recursive formula $f(n + 1)=1.5f(n)$ indicates a geometric sequence with a common ratio $r = 1.5$. To check which sequence is generated, divide each term by the previous term.

Step2: Check the first sequence

For the sequence $- 12,-18,-27,\cdots$, calculate the ratio of the second term to the first term: $\frac{-18}{-12}=1.5$, and the ratio of the third term to the second term: $\frac{-27}{-18}=1.5$.

Step3: Check the second sequence

For the sequence $-20,30,-45,\cdots$, the ratio of the second term to the first term is $\frac{30}{-20}=-1.5$.

Step4: Check the third sequence

For the sequence $-18,-16.5,-15,\cdots$, the ratio of the second term to the first term is $\frac{-16.5}{-18}=\frac{11}{12}\neq1.5$.

Step5: Check the fourth sequence

For the sequence $-16,-17.5,-19,\cdots$, the ratio of the second term to the first term is $\frac{-17.5}{-16}=\frac{35}{32}\neq1.5$.

Answer:

$-12,-18,-27,\cdots$