what is the common ratio for the geometric sequence below, written as a fraction? 768, 480, 300, 187.5, ...

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's take the second term $a_{2}=480$ and the first term $a_{1}=768$. Then $r=\frac{a_{2}}{a_{1}}=\frac{480}{768}$.

Step3: Simplify the fraction

We can simplify $\frac{480}{768}$ by finding the greatest common divisor (GCD) of 480 and 768. The GCD of 480 and 768 is 96. Dividing both the numerator and the denominator by 96, we get $\frac{480\div96}{768\div96}=\frac{5}{8}$.

Answer:

$5/8$