Question

Is 3, 1, 1/3, 1/9,... a geometric sequence?

Answer 1

$a_1;\ a_2;\ a_3;\ a_3;\ ...;\ a_n;\ a_{n+1};...\ is\ a\ geometric\ sequence\\if\ a_{n+1}:a_n=const.\\-------------------\\a_1=3;\ a_2=1;\ a_3=\dfrac{1}{3};\ a_4=\dfrac{1}{9}\\\\a_4:a_3=\dfrac{1}{9}:\dfrac{1}{3}=\dfrac{1}{9}\cdot\dfrac{3}{1}=\dfrac{1}{3}\\\\a_3:a_2=\dfrac{1}{3}:1=\dfrac{1}{3}\\\\a_2:a_1=1:3=\dfrac{1}{3}\\\\Answer:Yes.\ It's\ the\ geometric\ sequence.$