Let \(F_n \) denote the \(n^\text{th} \) Fibonacci number. If we know that \({ F }_{ 24 }=46368\) and \({ F }_{ 28 }=317811\), then compute \({ F }_{ 26 }\).

**Details and Assumptions:**

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

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