Question

What is the 10th term of the geometric sequence 400, 200, 100...?

Answer 1

ANSWER

$a_ {10} = \frac{25}{32}$

EXPLANATION

The given geometric sequence is

400, 200, 100...

The first term is

$a_1=400$

The common ratio is

$r = \frac{200}{400} = \frac{1}{2}$

The nth term is

$a_n=a_1( {r}^{n - 1} )$

We substitute the known values to get;

$a_n=400( \frac{1}{2} )^{n - 1}$

$a_ {10} =400( \frac{1}{2} )^{10 - 1}$

$a_ {10} =400( \frac{1}{2} )^{9}$

$a_ {10} = \frac{25}{32}$