Question

Help!! at least take a look

What is the recursive rule for this geometric sequence?

27,  9,  3,  1,  ...

Enter your answers in the boxes.

an= ⋅an−1

a1=

Answer 1

A recursive rule for a geometric sequence:

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

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