**Determine whether this statement about Fibonacci numbers is true. 2πΉπ β πΉπβ2 = πΉπ+1 for x> 1 where πΉπ is the ππ‘β Fibonacci number.**

The **Answer to the Question**

is below this banner.

**Here's the Solution to this Question**

LetΒ $x$Β any positive integer. IfΒ $F_x$Β is what we use to describe theΒ $x$th Fibonacci number, then

$F_x = F_{xβ1} + F_{xβ2}$

Then

$F_{x+1} = F_{x} + F_{xβ1}=F_{x}+(F_{x}-F_{x-2})$

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

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