Question

What is the recursive rule for this geometric sequence?

1, 3, 9, 27, ...

Enter your answers in the boxes.

Answer 1

A recursive rule for a geometric sequence:

`a_1\\a_n=r\cdot a_(n-1)`

`a_1=1,\ a_2=3,\ a_3=9,\ a_4=27\\\\r=(a_(n+1))/(a_n)\to r=(a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)\to r=(3)/(1)=(9)/(3)=(27)/(9)=3\\\\\boxed{a_1=1,\qquad a_n=3\cdot a_(n-1)}`