Answer
The sequence is geometric.
The common ratio is $r=\dfrac{1}{2}$.
Work Step by Step
A geometric sequence has a common ratio $r$. The common ratio is multiplied to the current term to get the next term of the sequence.
The common ratio is equal to the the quotient of a term and the term before it.
Solve for the ratio of each pair of consecutive terms to obtain:
$\dfrac{\frac{3}{2}}{3} = \dfrac{3}{6}=\dfrac{1}{2}
\\\dfrac{\frac{3}{4}}{\frac{3}{2}}=\dfrac{3}{4} \cdot \dfrac{2}{3} = \dfrac{1}{2}
\\\dfrac{\frac{3}{8}}{\frac{3}{4}} = \dfrac{3}{8} \cdot \dfrac{3}{4}=\dfrac{1}{2}$
Since the ratio is common to all pairs of consecutive terms, then the sequence is geometric.
The common ratio is $r=\dfrac{1}{2}$.
