Question

Pablo generates the function f (x) = three-halves (five-halves) superscript x minus 1 to determine the xth number in a sequence. which is an equivalent representation? f(x 1) = five-halvesf(x) f(x) = five-halvesf(x 1) f(x 1) = three-halvesf(x) f(x) = three-halvesf(x 1)

Answer 1

The $x^{th}$ number in the sequence will be   $F[x]=\dfrac{5}{2} F[x]$

What will be the xth number in the sequence?

The given function is

$F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}$

Now at  $x=x+1$ for the function

$F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x+1-1}$

$F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x }$

Now we can write

$F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1} \dfrac{5}{2}^1$

Since     $F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}$

so

$F[x]=\dfrac{5}{2} F[x]$

Thus the $x^{th}$ number in the sequence will be   $F[x]=\dfrac{5}{2} F[x]$

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Answer 2

Answer:

A

Step-by-step explanation:

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