Question

What is the recursive rule for this geometric sequence? 2, 1/2, 1/8,  1/32,  

Enter your answers in the blanks.

an= _ ⋅an−1

a1=_

Answer 1

`a_1=2,\ a_2=(1)/(2),\ a_3=(1)/(8);\ a_4=(1)/(32)\\\\r=(a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)=...\\\\r=((1)/(2))/(2)=((1)/(8))/((1)/(2))=((1)/(32))/((1)/(8))=(1)/(4)\\\\\boxed{a_1=2;\qquad a_n=(1)/(4)\cdot a_(n-1)}`