Answer:
[tex]a_n = 3 ({5})^{n - 1} [/tex]
Step-by-step explanation:
The given sequence is 3,15,75,375,...
The first term of this geometric sequence is
[tex]a_1=3[/tex]
The common ratio is
[tex]r = \frac{15}{3} = 5[/tex]
The explicit formula is given by:
[tex]a_n = a_1 {r}^{n - 1} [/tex]
We plug the first term and common ratio into the formula to get:
[tex]a_n = 3 ({5})^{n - 1} [/tex]
