natalia is writing a recursive formula to represent the sequence. 8, 12, 18, 27, ... what value should she…

Explanation:

Step1: Recall common - ratio formula

The common ratio $r$ of a geometric sequence is given by $r=\frac{a_{n + 1}}{a_{n}}$, where $a_{n+1}$ is the $(n + 1)$ - th term and $a_{n}$ is the $n$ - th term.

Step2: Calculate the common ratio

Let $a_{1}=8$ and $a_{2}=12$. Then $r=\frac{a_{2}}{a_{1}}=\frac{12}{8}=\frac{3}{2}$. We can double - check with other consecutive terms. Let $a_{2}=12$ and $a_{3}=18$, then $r = \frac{a_{3}}{a_{2}}=\frac{18}{12}=\frac{3}{2}$. Let $a_{3}=18$ and $a_{4}=27$, then $r=\frac{a_{4}}{a_{3}}=\frac{27}{18}=\frac{3}{2}$.

Answer:

C. $\frac{3}{2}$