Determine whether this statement about Fibonacci numbers is true. 2𝐹𝒙 − 𝐹𝒙−2 = 𝐹𝒙+1 for x> 1 where 𝐹𝒙 is the 𝒙𝑡ℎ Fibonacci number.

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Let $x$ any positive integer. If $F_x$ is what we use to describe the $x$ th Fibonacci number, then

$F_x = F_{x−1} + F_{x−2}$

Then

$F_{x+1} = F_{x} + F_{x−1}=F_{x}+(F_{x}-F_{x-2})$

$=2F_{x}-F_{x-2}$

The statement $F_{x+1} =2F_{x}-F_{x-2}$ is true.