Which of the following is the common ratio of the geometric sequence $27, 9, 3, 1, \dfrac{1}{3}, \dfrac{1}{9}, \ldots$?

The common ratio of a geometric sequence is the **ratio of any term to the previous term**: $r = \dfrac{a_{2}}{a_{1}} = \dfrac{9}{27} = \dfrac{1}{3}$. Verify with the next pair: $\dfrac{3}{9} = \dfrac{1}{3}$ ✓. And $\dfrac{1}{3}$ — i.e. $\dfrac{1/3}{1} = \dfrac{1}{3}$ ✓. - Trap B ($3$) is the *reciprocal* of the correct ratio — you get this if you divide previous term by current term instead. - Trap A ($-3$) flips the sign and inverts. - Trap D ($1/9$) divides a non-adjacent pair (e.g. $a_{3}/a_{1} = 3/27$). The sequence is *decreasing* and stays *positive*, so the ratio must be a positive number strictly between $0$ and $1$.