To find a common ratio when given terms in a geometric sequence, divide terms based on their order, such as the following (where [tex] a_n [/tex] is the [tex] n [/tex]th term in the sequence and [tex] r [/tex] is the common ratio):
[tex] r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} = \dfrac{a_5}{a_4} [/tex]
In the problem above, we can find the common ratio by this method:
[tex] \dfrac{16}{64} = \dfrac{4}{16} = r = \dfrac{1}{4} [/tex]
In our geometric sequence, the common ratio is [tex] \boxed{\dfrac{1}{4}} [/tex].
