In a geometric sequence each term is found by multiplying the previous term by a constant.
To find the nth term in a geometric sequence we use:
[tex]a_n=ar^{n-1}[/tex]where a is the first term and r is the common ratio.
To find the common ratio we can divide the second term by the first:
[tex]\frac{1}{-3}=-\frac{1}{3}[/tex]and the third one by the second:
[tex]\frac{-\frac{1}{3}}{1}=-\frac{1}{3}[/tex]we notice that this in fact is the common ratio. Now we plug it in the formula above, therefore the geometric sequence is:
[tex]a_n=-3(-\frac{1}{3})^{n-1}[/tex]