Question

What is the explicit rule for the geometric sequence? 25.5, 5.1, 1.02, 0.204, ... an=25.5(15)n an=25.5(15)n−1 an=25.5(15)n+1 an=25.5(15)n+2

Answer 1

Given:

The geometric sequence is:

25.5, 5.1, 1.02, 0.204, ...

To find:

The explicit rule for the given geometric sequence.

Solution:

We have,

25.5, 5.1, 1.02, 0.204, ...

Here, the first term is 25.5 and the common ratio is:

`r=(a_2)/(a_1)`

`r=(5.1)/(25.5)`

`r=(1)/(5)`

The explicit rule for a geometric sequence is:

`a_n=ar^(n-1)`

Where, a is the first term and r is the common ratio.

Putting
`a=25.5,\ r=(1)/(5)` in the above formula, we get

`a_n=25.5((1)/(5))^(n-1)`

Therefore, the correct option is B.