Using this formula,
[tex]r=\frac{a_{n+1}}{a_n}[/tex]
and by substituting n to any number (except for its last term because next to it in a sequence, there's nothing else or its endless).
Common ratio:
Let [tex]n=1[/tex] and [tex]2[/tex].
For [tex]n=1[/tex],
[tex]r_1=\frac{a_{1+1}}{a_1}[/tex]
[tex]r_1=\frac{a_{2}}{a_1}[/tex]
[tex]r_1=\frac{\frac{2}{7}}{\frac{4}{7} }[/tex]
[tex]r_1=\frac{2}{7}*{\frac{7}{4}[/tex] (reduce to lowest terms if possible)
[tex]r_1=\frac{1}{1}*{\frac{1}{2}[/tex]
[tex]r_1={\frac{1}{2}[/tex]
and for [tex]n=2[/tex]
[tex]r_2=\frac{a_{2+1}}{a_2}[/tex]
[tex]r_2=\frac{a_{3}}{a_2}[/tex]
[tex]r_2=\frac{\frac{1}{7}}{\frac{2}{7}}[/tex]
[tex]r_2=\frac{1}{7}*\frac{7}{2}[/tex]
[tex]r_2=\frac{1}{1}*\frac{1}{2}[/tex]
[tex]r_2=\frac{1}{2}[/tex]
As you can see, both of ratios [tex]r_1[/tex] and [tex]r_2[/tex] are the same. (You can go further if you want to) Therefore, to conclude, it is a geometric sequence and its common ratio is 1/2.
