recall that in a geometric sequence, you multiply the "current" one by the common ratio to get the "next" so, if you divide "next"/"current", the quotient is just the common ratio,
[tex]\bf \cfrac{27}{243}=\cfrac{3}{27}=\cfrac{\frac{1}{3}}{3}=\cfrac{\frac{1}{27}}{\frac{1}{3}}\implies \cfrac{1}{9}\impliedby \textit{common ratio}[/tex]
notice, all we did was, divide the value, by the number to its left-hand-side.
