Question

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, ...}.

Answer 1

`f(x) = 3 * {2}^(x)`

Answer 2

`f(x)=(3)/(2)(2)^x`

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

`f(x)=ab^x` ...(1)

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

`3=ab^1` ....(i)

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

`6=ab^2` ....(ii)

Divide equation (ii) by (i).

`(6)/(3)=(ab^2)/(ab)`

`2=b`

Substitute b=2 in equation (1).

`3=a(2)^1`

`(3)/(2)=a`

Substitute
`a=(3)/(2)` and
`b=2` in (1).

`f(x)=(3)/(2)(2)^x`

Therefore, the required function is
`f(x)=(3)/(2)(2)^x`.