Question

Sebastian 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

We have ratio 4 and f(2)=12. Let f(1)=a. Then f(2)=a·4 = 12 ⇒ a = 3. So the explicit formula is f(x) = 3·4^(x−1). (Second choice.)