Middle Fibonacci Number

Let FnF_n denote the nthn^\text{th} Fibonacci number. If we know that F24=46368{ F }_{ 24 }=46368 and F28=317811{ F }_{ 28 }=317811, then compute F26{ F }_{ 26 }.

Details and Assumptions:

  • A Fibonacci sequence is a sequence that satisfy the recurrence relation Fn+2=Fn+1+FnF_{n+2} = F_{n+1} + F_n for Fn1F_n \geq 1 with initial conditions F1=F2=1F_1 = F_2 = 1 .
  • No tables nor calculators are required to solve this problem.
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