Question

ebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12.

Which explicit formula can be used to model the same sequence?

f(x) = 12(4)x
f(x) = 3(4)x − 1
f(x) = 4(12)x
f(x) = 4(3)x − 1

Answer 1

Recursive rule f(x+1)=4f(x) has ratio 4. Let f(1)=a. Then f(2)=4a=12, so a=3. The explicit formula is

f(x)=3·4^(x−1).

(That corresponds to the second choice.)