# What is the common ratio of the geometric sequence 1, 4, 16, 64,...?

May 18, 2015

The geometric sequence given is:
$1 , 4 , 16 , 64$ ...

The common ratio $r$ of a geometric sequence is obtained by dividing a term by its preceding term

as follows:
1) $\frac{4}{1} = 4$
2) $\frac{16}{4} = 4$

for this sequence the common ratio $r = 4$

Likewise the next term of a geometric sequence can be obtained by multiplying the particular term by $r$

Example in this case the term after $64 = 64 \times 4 = 256$