Question

What is f(5) if f(1) = 3.2 and f(x + 1) = (f(x))?

Answer 1

`f(x + 1) = (5/2)*f(x) f(x + 1) = 2.5*f(x), f(1) = 3.2 f(2) = 2.5f(1) = 2.5*3.2 = 8 f(3) = 2.5f(2) = 2.5*8 = 20 f(4) = 2.5f(3) = 2.5*20 = 50 f(5) = 2.5f(4) = 2.5*50 = 125`

Answer 2

`f(5)=125`

Explanation:

The complete question is

What is f(5) if f(1) = 3.2 and f(x + 1) =5/2 (f(x))?

By given,

`f(1)=3.2` and
`f(x+1)=(5)/(2)(f(x))`

Now, we need to replace one be one until we get
`f(5)`, because the given function is a sequence, so

For
`x=1`

`f(x+1)=(5)/(2)(f(x))`

`f(1+1)=(5)/(2)(f(1))\\f(2)=2.5(3.2)=8`

Then, for
`x=2`

`f(2+1)=(5)/(2)(f(2))\\f(3)=2.5(8)=20`

We repeat the process until we get
`f(5)`,

For
`x=3`

`f(3+1)=(5)/(2)(f(3))\\f(4)=2.5(20)=50`

For
`x=4`

`f(4+1)=(5)/(2)(f(4))\\f(5)=2.5(50)=125`

Therefore, if
`f(1)=3.2` and
`f(x+1)=(5)/(2)(f(x))`, then
`f(5)=2.5(50)=125`