Question

HELP PLZ! THIS IS TIMED.

Answer 1

`b_n=(2)/(3)\cdot (9)^(n-1)`

Explanation:

Given the geometric sequence

`a_1=(2)/(3)\\ \\a_n=3a_(n-1),`

then

`a_1=(2)/(3)\\ \\a_2=3a_1=3\cdot (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\\ \\...`

Hence,

`b_1=a_1=(2)/(3)\\ \\b_2=a_3=6=(2)/(3)\cdot 9\\ \\b_3=a_5=54=(2)/(3)\cdot 9^2\\ \\...`

Thus, the explicit formula is

`b_n=(2)/(3)\cdot (9)^(n-1)`