To calculate the 23rd Fibonacci number, \( F(23) \), we follow the Fibonacci sequence definition, where each number is the sum of the two preceding ones:

\[
F(n) = F(n-1) + F(n-2)
\]

with the initial conditions \( F(0) = 0 \) and \( F(1) = 1 \).

Calculating step-by-step:

\[
\begin{aligned}
&F(0) = 0, \\
&F(1) = 1, \\
&F(2) = 1, \\
&F(3) = 2, \\
&F(4) = 3, \\
&F(5) = 5, \\
&F(6) = 8, \\
&F(7) = 13, \\
&F(8) = 21, \\
&F(9) = 34, \\
&F(10) = 55, \\
&F(11) = 89, \\
&F(12) = 144, \\
&F(13) = 233, \\
&F(14) = 377, \\
&F(15) = 610, \\
&F(16) = 987, \\
&F(17) = 1597, \\
&F(18) = 2584, \\
&F(19) = 4181, \\
&F(20) = 6765, \\
&F(21) = 10946, \\
&F(22) = 17711, \\
&F(23) = 28657.
\end{aligned}
\]

Thus, \( F(23) = 28,657 \).

Would you like further details or have any questions?

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Here are five related questions to expand on this topic:

1. How do you derive the closed-form expression for the Fibonacci sequence?
2. What is the significance of the golden ratio in the Fibonacci sequence?
3. Can you explain the relationship between Fibonacci numbers and Pascal's Triangle?
4. How do Fibonacci numbers appear in nature?
5. What are some applications of the Fibonacci sequence in computer science?

**Tip:** The Fibonacci sequence grows exponentially, and you can use matrix exponentiation to compute large Fibonacci numbers efficiently.

Learn how to calculate the 23rd Fibonacci number (F(23)) using the Fibonacci sequence formula. Follow a detailed step-by-step solution and understand the recursive nature of Fibonacci numbers. Suitable for students and enthusiasts interested in mathematical sequences.

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