Question

Pablo generates the function f(x) = 3/2(5/2)^x-1 to determine the x'th number in a sequence.

Which is an equivalent representation?

A: f(x+1) = 5/2 f(x)
B: f(x) = 5/2 f(x+1)
C: f(x+1) 3/2 f(x)
D: f(x+1) = 3/2 f(x+1)

Answer 1

A

Explanation:

Edge 2021

Answer 2

A.

f(x+1)=5/2f(x) with f(1)=3/2

Explanation:

So we are looking for a recursive form of

`f(x)=(3)/(2)((5)/(2))^(x-1)`.

This is the explicit form of a geometric sequence where
`r=5/2` and
`a_1=(3)/(2)`.

The general form of an explicit equation for a geometric sequence is

`a_1(r)^(n-1) \text{ where } a_1 \text{ is the first term and } r \text{ is the common ratio}`.

The recursive form of that sequence is:

`a_(n+1)=ra_n \text{ where you give the first term value for } a_1`.

So we have r=5/2 here so the answer is A.

f(x+1)=5/2f(x) with f(1)=3/2

By the way all this says is term is equal to 5/2 times previous term.