Answer:
[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]
Step-by-step explanation:
Given the geometric sequence
[tex]a_1=\dfrac{2}{3}\\ \\a_n=3a_{n-1},[/tex]
then
[tex]a_1=\dfrac{2}{3}\\ \\a_2=3a_1=3\cdot \dfrac{2}{3}=2\\ \\a_3=3a_2=3\cdot 2=6\\ \\a_4=3a_3=3\cdot 6=18\\ \\a_5=3a_4=3\cdot 18=54\\ \\...[/tex]
Hence,
[tex]b_1=a_1=\dfrac{2}{3}\\ \\b_2=a_3=6=\dfrac{2}{3}\cdot 9\\ \\b_3=a_5=54=\dfrac{2}{3}\cdot 9^2\\ \\...[/tex]
Thus, the explicit formula is
[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]
