Answer:
B. gives the required expression.
Step-by-step explanation:
The question is incomplete. Here is the complete 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
Given the recursive formula f(x+1) = 4f(x) and second term is 12 then f(2) = 12
If x =2
f(2+1) =4f(2)
f(3)= 4f(2)
f(3)= 4*12
f(3) = 48
if x = 3
f(3+1) =4f(3)
f(4)= 4f(3)
f(4)= 4*48
f(4) = 192
To get the first term, we will substitute x = 1 into the recursive function;
f(1+1) =4f(1)
f(2) = 4f(1)
since f(2) = 12 then f(2) = 4f(1) = 12
f(1) = 12/4 = 3
The sequence formed by the first four terms of recursive function is 3, 12, 48, 192... which gives a geometric sequence.
The xth term of a geometric sequence is expressed as where a is the first term and r is the common ratio.
from the sequence above a is 3 and r = 12/3 = 48/12 = 194/48 = 4
Substituting this value into the nth term of the sequence;
This gives the required expression.