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=\dfrac{a_2}{a_1}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Ba_2%7D%7Ba_1%7D)
![r=\dfrac{5.1}{25.5}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B5.1%7D%7B25.5%7D)
![r=\dfrac{1}{5}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B1%7D%7B5%7D)
The explicit rule for a geometric sequence is:
![a_n=ar^{n-1}](https://tex.z-dn.net/?f=a_n%3Dar%5E%7Bn-1%7D)
Where, a is the first term and r is the common ratio.
Putting
in the above formula, we get
![a_n=25.5(\dfrac{1}{5})^{n-1}](https://tex.z-dn.net/?f=a_n%3D25.5%28%5Cdfrac%7B1%7D%7B5%7D%29%5E%7Bn-1%7D)
Therefore, the correct option is B.