Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12. choose the explicit formula that can be used to model the same sequence.
a.) f(x) = 12(4)x
b.) f(x) = 3(4)x − 1
c.) f(x) = 4(12)x
d.) f(x) = 4(3)x − 1

The best and most correct answer among the choices provided by your question is the second choice or letter B. The formula can be f(x) = 3(4)x − 1


If f(2)=12 then f(2+1)=4(12) Now go to the general formula for a geometric sequence.an=a1∗r(n−1)

Since f(3)=48 and f(2)=12 or you can say
a3=48anda2=12
Sincer=an+1an
then r= 48/12 or 4 Now finda1
from the formula for n=348=a1∗4(3−1)
Soa1=3
So it looks likef(x)=3∗4x−1