8.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

Question

8.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

misssunshinexxoxo · Answer

Which one do you believe it is?

jaylelile · Answer

I come up with different answers every time

anonymous · Answer

If f(2)=12 then f(2+1)=4(12)

Now go to the general formula for a geometric sequence.

$$a _{n}=a _{1}*r ^{(n-1)}$$ Since f(3)=48 and f(2)=12  or you can say $$a _{3}=48$$ and $$a _{2}=12$$
Since  $$r=\frac{ a _{n +1} }{ a _{n} }$$then r= 48/12 or 4

Now find $$a _{1}$$ from the formula for n=3

$$48=a _{1}*4^{(3-1)}$$ So $$a _{1}=3$$

So it looks like $$f(x)=3*4^{x-1}$$