Question

1. 192, 24, 3, \frac{3}{8},...

ometric: yes or no (circle your choice)
geometric, what is r?

Explanation:

Step1: Check if it is a geometric sequence

In a geometric sequence, the ratio \(r\) between consecutive terms is constant.
Let's find the ratio between the second and the first term: \(r_1=\frac{24}{192}=\frac{1}{8}\)

Step2: Check the ratio between the third and the second term

\(r_2 = \frac{3}{24}=\frac{1}{8}\)

Step3: Check the ratio between the fourth and the third term

\(r_3=\frac{\frac{3}{8}}{3}=\frac{3}{8}\times\frac{1}{3}=\frac{1}{8}\)

Since the ratio between consecutive terms is constant (\(r = \frac{1}{8}\)), the sequence is geometric.

Answer:

Yes, \(r=\frac{1}{8}\)