The Fibonacci Sequence

What this Fibonacci formula interview question tests

This is an easy puzzle that appears in quant interviews to assess whether you can derive a closed-form expression from a recurrence relation. It rewards mathematical insight and familiarity with standard techniques rather than brute-force computation.

Candidates are expected to recognize the Fibonacci recurrence and convert it into an explicit formula. The solution involves setting up a characteristic equation, solving for roots, and using initial conditions to pin down coefficients. Interviewers use this to gauge comfort with linear recurrences and whether you can work cleanly through algebraic manipulation.

• Characteristic equations and eigenvalues of recurrence relations
• Solving systems of linear equations for unknown coefficients
• Recognizing when a closed form is more useful than iterative computation