Answer
The sequence is geometric.
The common ratio is $r=-\dfrac{1}{3}$.
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:
$\dfrac{-144}{432} = -\dfrac{1}{3}
\\\dfrac{48}{-144}=-\dfrac{1}{3}
\\\dfrac{-16}{48} = -\dfrac{1}{3}$
Since the ratio is common to all pairs of consecutive terms, then the sequence is geometric.
The common ratio is $r=-\dfrac{1}{3}$.
