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:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{5.1}{25.5}[/tex]
[tex]r=\dfrac{1}{5}[/tex]
The explicit rule for a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]a=25.5,\ r=\dfrac{1}{5}[/tex] in the above formula, we get
[tex]a_n=25.5(\dfrac{1}{5})^{n-1}[/tex]
Therefore, the correct option is B.
