# Fibonacci squares

Algebra Level 2

$\large 1,1,2,3,5,8,13,21,34,55,89, \cdots$

The above is the Fibonacci sequence, where $$F_n$$ is the $$n$$th Fibonacci number with $$F_1 = F_2 = 1$$.

Without using a calculator, find which answer is equivalent to $${ ({ F }_{ 10 }) }^{ 2 }-{ ({ F }_{ 9 }) }^{ 2 }$$.



Hint: Try to find a simpler formula for $${ ({ F }_{ n+1 }) }^{ 2 }-{ ({ F }_{ n }) }^{ 2 }$$.

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