We have to write this model as a geometric sequence.
We know that the first term will have a value of 15, corresponding to the distance of the first swing.
Then, the second term will be 0.85 (or 85%) of the first term. This gives us the ratio of the geometric sequence:
[tex]r=\frac{a_2}{a_1}=0.85[/tex]
Then, we can find the explicit formula as:
[tex]\begin{gathered} a_1=15 \\ a_2=r\cdot a_1=0.85\cdot15 \\ a_3=r\cdot a_2=r^2\cdot a_1=(0.85)^2\cdot15 \\ a_n=r\cdot a_{n-1}=r^{n-1}\cdot a_1=(0.85)^{n-1}\cdot15 \\ a_n=15\cdot(0.85)^{n-1} \end{gathered}[/tex]
Answer: an = 15*(0.85)^(n-1) [Option B]
