Question

In the exercise, determine if the sequence is geometric, and if so, indicate the common ratio.

$48,24,12,6,3,\frac{3}{2},...$

Short answer

The sequence is geometric with common ratio equal to$\frac{1}{2}$.

Step-by-step solution

Step 1. Given information

The sequence is$48,24,12,6,3,\frac{3}{2},...$

Step 2. Determine if the sequence is geometric, and if so, indicate the common ratio. 

Consider the sequence $48,24,12,6,3,\frac{3}{2},...$

role="math" localid="1645356554895" $\begin{array}{rcl}\frac{24}{48}& =& \frac{1}{2}\\ \frac{12}{24}& =& \frac{1}{2}\\ \frac{6}{12}& =& \frac{1}{2}\\ \frac{3}{6}& =& \frac{1}{2}\\ \frac{{\displaystyle \frac{3}{2}}}{3}& =& \frac{1}{2}\end{array}$

So, the sequence is geometric with common ratio equal to$\frac{1}{2}$.