so... for a geometric sequence, a common ratio, is that "something" you multiply the current term's value, to get the next term's value
now, if you simply divide any of the terms by the guy behind them, you'd get the common ratio
namely [tex]\bf a,a\cdot b\qquad \qquad \cfrac{a\cdot b}{a}=b\impliedby common\ ratio[/tex]
hmm so hmmm let's say let's take 1/8 and -1/4, we could use any pair of subsequent terms, but let's just use those two anyway
[tex]\bf \cfrac{\frac{1}{8}}{-\frac{1}{4}}\implies \cfrac{1}{8}\cdot \cfrac{4}{-1}\implies -\cfrac{1}{2}\impliedby \textit{common ratio}[/tex]
