Given the geometric sequence:
[tex]-\frac{1}{2},\frac{3}{4},\frac{-9}{8},\ldots.[/tex]
The common ratio will be:
[tex]r=\frac{3}{4}\div-\frac{1}{2}=\frac{3}{4}\cdot-2=-\frac{3}{2}[/tex]
The general rule of the geometric sequence will be:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
so, a7 will be:
[tex]a_7=-\frac{1}{2}\cdot(-\frac{3}{2})^{7-1}=-\frac{1}{2}\cdot(-\frac{3}{2})^6=-\frac{729}{128}[/tex]
And an will be:
[tex]a_n=(-\frac{1}{2})\cdot(-\frac{3}{2})^{n-1}_{}[/tex]
