Question

What is the explicit rule for this geometric sequence?

2/9,2/3,2,6,...




an=3(2/9)^n−1

an=2/9⋅3^n−1

an=2/9⋅3^n

an=3(2/9)n

Answer 1

`a_1=(2)/(9),\ a_2=(2)/(3),\ a_3=2,\ a_4=6,\ ...\\\\r=a_2:a_1\\\\r=(2)/(3):(2)/(9)=(2)/(3)\cdot(9)/(2)=3\\\\a_n=a_1r^(n-1)\\\\\boxed{a_n=(2)/(9)\cdot3^(n-1)}`