Answer
$a_n=(\dfrac{1}{4})^{n-2}$
Work Step by Step
The $n^{th}$ term of the geometric sequence is given by the formula:
$ a_n=a_1r^{n-1}$
where $r$=common ratio and $a_1$= the first term
The common ratio of a geometric sequence is equal to the quotient (ratio) of any term and the term before it:
$ \ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}$
Here, we have: $a_1= 4$ and $a_2=1$, so $r=\dfrac{1}{4}$
Thus, the general formula for the given sequence is:
$a_n=4(\dfrac{1}{4})^{n-1}=(\dfrac{1}{4})^{n-2}$
