Answer
The geometric sequence and the common ratio is $ r=\dfrac{1}{2}$.
Work Step by Step
We are given that $ a_n=(\dfrac{1}{2})^n $
Here, we have the first four terms $ a_1=\dfrac{1}{2}, a_2=\dfrac{1}{4},a_3=\dfrac{1}{8},a_4=\dfrac{1}{16}$ when $ n=1,2,3,4$
Now, subtract each two consecutive terms as below: $ a_2/a_1=\dfrac{1/4}{1/2}=\dfrac{1}{2}; a_3/a_2=\dfrac{1}{2}; a_4/a_3=\dfrac{1/16}{1/8}=\dfrac{1}{2}$
We can see that this is the geometric sequence and the common ratio is $ r=\dfrac{1}{2}$.
