Answer:
Option C)
Explanation:
To know which is the explicit formula we will replace n = 2 and n = 5. If we get 6 and 162 respectively, we can say that it is the correct formula.
For option A)
[tex]\begin{gathered} a_n=\frac{2}{15}\cdot5^{n-1} \\ \\ \text{ If n = 2} \\ a_2=\frac{2}{15}\cdot5^{2-1}=\frac{2}{15}\cdot5^1=\frac{2}{15}\cdot5=\frac{2}{3} \end{gathered}[/tex]
Since 2/3 is different from 6, we get that this is not the correct answer
For option B)
[tex]\begin{gathered} a_n=\frac{2}{3}\cdot5^{n-1} \\ \\ a_2=\frac{2}{3}\cdot5^{2-1}=\frac{2}{3}\cdot5=\frac{10}{3} \end{gathered}[/tex]
Since 10/3 is different from 6, we get that this is not the correct answer
For option C)
[tex]\begin{gathered} a_n=2\cdot3^{n-1} \\ a_2=2\cdot3^{2-1}=2\cdot3^1=6 \\ a_5=2\cdot3^{5-1}=2\cdot3^4=2\cdot81=162 \end{gathered}[/tex]
Therefore, the answer is option C)
