Question

homework assignment 9.3 geometric sequences
due friday by 11:59pm points 13 submitting an external tool
homework assignment 9.3 geometric sequences
score: 1/13 answered: 1/13
question 2
determine whether the sequence is arithmetic, geometric or neither.
\\(\frac{1}{3}, \frac{1}{12}, \frac{1}{48}, \frac{1}{192}, \frac{1}{768}, \dots\\)
select an answer
if the sequence is geometric, what is the common ratio?
question help: video written example

Explanation:

Step1: Check for arithmetic sequence

Calculate differences between terms: $\frac{1}{12}-\frac{1}{3}=-\frac{1}{4}$, $\frac{1}{48}-\frac{1}{12}=-\frac{1}{16}$. Differences are not constant.

Step2: Check for geometric sequence

Calculate ratios between terms: $\frac{1/12}{1/3}=\frac{1}{4}$, $\frac{1/48}{1/12}=\frac{1}{4}$, $\frac{1/192}{1/48}=\frac{1}{4}$, $\frac{1/768}{1/192}=\frac{1}{4}$. Ratios are constant.

Answer:

Geometric; common ratio is $\frac{1}{4}$