Answer
The common ratio for the geometric sequence $75,15,3,\frac{3}{5},\ldots $ is $r=\frac{1}{5}$.
Work Step by Step
$75,15,3,\frac{3}{5},\ldots $
Thus,
$\begin{align}
& r=\frac{{{a}_{1+1}}}{{{a}_{1}}} \\
& =\frac{{{a}_{2}}}{{{a}_{1}}} \\
& =\frac{15}{75} \\
& =\frac{1}{5}
\end{align}$
Thus, the common ratio for the geometric sequence $75,15,3,\frac{3}{5},\ldots $ is $r=\frac{1}{5}$.
