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)

Accepted Solution

The [tex]x^{th}[/tex] number in the sequence will be   [tex]F[x]=\dfrac{5}{2} F[x][/tex]What will be the xth number in the sequence?The given function is [tex]F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}[/tex]Now at  [tex]x=x+1[/tex] for the function [tex]F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x+1-1}[/tex][tex]F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x }[/tex]Now we can write [tex]F[x+1]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1} \dfrac{5}{2}^1[/tex]Since     [tex]F[x]=\dfrac{3}{2} \times \dfrac{5}{2}^{x-1}[/tex]so [tex]F[x]=\dfrac{5}{2} F[x][/tex]Thus the [tex]x^{th}[/tex] number in the sequence will be   [tex]F[x]=\dfrac{5}{2} F[x][/tex]To know more about Functions follow