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 \({ ({ F }_{ n+1 }) }^{ 2 }-{ ({ F }_{ n }) }^{ 2 }\).

\[{ 21 }^{ 2 }\] \[{ 34 }^{ 2 }+{ 13 }\] \[89\cdot 21\] \[55\cdot { 13 }^{ 2 }\] \[{ 34 }^{ 2 }+{ 13 }^{ 2 }\] \[{ 34 }^{ 2 }\] \[55\cdot 13\] \[55\cdot 21\]

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.