First let's find the ratio of the sequence, by dividing one term by the term before:
[tex]\begin{gathered} \text{second term: 15} \\ \text{first term: 75} \\ ratio=\frac{15}{75}=\frac{1}{5} \end{gathered}[/tex]So the ratio is 1/5 and the first term is 75.
Now, we can use the following formula for the nth term of a geometric sequence:
[tex]a_n=a_1\cdot q^{n-1}[/tex]Where q is the ratio and a1 is the first term. So we have:
[tex]a_n=75(\frac{1}{5})^{n-1}[/tex]Substituting an by the function f(n), we have:
[tex]f(n)=75(\frac{1}{5})^{n-1}[/tex]So the correct option is b)
