Given that a geometric sequence can be expressed as a non-linear function in the form f(x) = abx, write a non-linear function to describe the sequence {3, 6, 12, 24, 48, 96, }.

Step-by-step explanation:

The given sequence is

{3, 6, 12, 24, 48, 96, ...}

It means f(x)=3, 6, 12, 24, 48, 96, ... for x=1,2,3,4,5,6,.. respectively.

We need to find non-linear function in the form  

      ...(1)

We know that f(x)=3 for x=1.

         ....(i)

We know that f(x)=6 for x=2.

         ....(ii)

Divide equation (ii) by (i).

Substitute b=2 in equation (1).

Substitute and in (1).

Therefore, the required function is .