Question

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

Answer 1

`a_ {10} = (25)/(32)`

Step-by-step explanation

The given geometric sequence is

400, 200, 100...

The first term is

`a_1=400`

The common ratio is

`r = (200)/(400) = (1)/(2)`

The nth term is

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

We substitute the known values to get;

`a_n=400( (1)/(2) )^(n - 1)`

`a_ {10} =400( (1)/(2) )^(10 - 1)`

`a_ {10} =400( (1)/(2) )^(9)`

`a_ {10} = (25)/(32)`