## College Algebra 7th Edition

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: $\dfrac{\frac{1}{4}}{\frac{1}{2}} = \dfrac{1}{4} \cdot \dfrac{2}{1} =\dfrac{1}{2} \\\dfrac{\frac{1}{6}}{\frac{1}{4}}=\dfrac{1}{6} \cdot \dfrac{4}{1} = \dfrac{4}{6} = \dfrac{2}{3}$ The ratios are different so there is no need to compute for the ratio of the next pair. The sequence is not geometric.