Question

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

Answer 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

Answer 2

Answer : B.) f(x) =$f(x) = 3(4)^{n-1}$

The recursive formula f(x+1) = 4f(x)

Given : second term is 12 , so f(2) = 12

f(3) = 4f(2) = 4 * 12 = 48

f(4) = 4f(3) = 4*48 = 192

f(2) = 12 = 4* 3= 4*f(1). So f(1) = 3

f(1) =3 , f(2) = 12, f(3) = 48, f(4)=192.....

The sequence is Geometric

We use geometric sequence formula

$f(x) = ar^{n-1}$, where 'a' is the first term and 'r' is the common ratio

a= 3 and r= 4

Explicit formula is $f(x) = 3(4)^{n-1}$