Answer
Not a geometric sequence.
Work Step by Step
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Here: $a_1=\frac{1}{\sqrt1}=\frac{1}{1}=1$
$a_2=\frac{1}{\sqrt2}=\frac{\sqrt2}{2}$
$a_3=\frac{1}{\sqrt3}=\frac{\sqrt3}{3}$
$a_4=\frac{1}{\sqrt4}=\frac{1}{2}$
Thus we can see that the quotient is not constant, thus it is not a geometric sequence.