Given:
The sequence is 8, 10, 12.5, 15.625,...
To find:
The explicit formula for the given sequence.
Solution:
We have,
8, 10, 12.5, 15.625,...
Here, the first terms is 8.
[tex]\dfrac{10}{8}=1.25[/tex]
[tex]\dfrac{12.5}{10}=1.25[/tex]
[tex]\dfrac{15.625}{12.5}=1.25[/tex]
The common ratio is 1.25. So, the given sequence is a geometric sequence.
The explicit formula for a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The explicit formula for the given geometric sequence is:
[tex]a_n=8(1.25)^{n-1}[/tex]
Therefore, the correct option is A.
