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:

$a_1\\a_n=r\cdot a_{n-1}$

$a_1=1,\ a_2=3,\ a_3=9,\ a_4=27\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\to r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=3\\\\\boxed{a_1=1,\qquad a_n=3\cdot a_{n-1}}$