ANSWER
[tex]a_ {10} = \frac{25}{32} [/tex]
EXPLANATION
The given geometric sequence is
400, 200, 100...
The first term is
[tex]a_1=400[/tex]
The common ratio is
[tex]r = \frac{200}{400} = \frac{1}{2} [/tex]
The nth term is
[tex]a_n=a_1( {r}^{n - 1} )[/tex]
We substitute the known values to get;
[tex]a_n=400( \frac{1}{2} )^{n - 1} [/tex]
[tex]a_ {10} =400( \frac{1}{2} )^{10 - 1} [/tex]
[tex]a_ {10} =400( \frac{1}{2} )^{9} [/tex]
[tex]a_ {10} = \frac{25}{32} [/tex]
