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The problem asks for \( \text{Fib}(29) \), given:

\[
\text{Fib}(30) = 832,040 \quad \text{and} \quad \text{Fib}(28) = 317,811.
\]

Using the Fibonacci sequence property:

\[
\text{Fib}(n) = \text{Fib}(n-1) + \text{Fib}(n-2),
\]

we know that:

\[
\text{Fib}(30) = \text{Fib}(29) + \text{Fib}(28).
\]

Substitute the known values:

\[
832,040 = \text{Fib}(29) + 317,811.
\]

Now, solve for \( \text{Fib}(29) \):

\[
\text{Fib}(29) = 832,040 - 317,811 = 514,229.
\]

Thus, \( \text{Fib}(29) = 514,229 \).

Would you like more details or have any questions?

Here are some related questions for deeper understanding:
1. How do we derive the general formula for Fibonacci numbers?
2. What is the time complexity for calculating Fibonacci numbers using recursion?
3. Can you explain the concept of memoization in the context of Fibonacci calculation?
4. How do you apply matrix exponentiation to find Fibonacci numbers efficiently?
5. What is the golden ratio's connection to the Fibonacci sequence?

**Tip:** When calculating Fibonacci numbers for large values, iterative methods or matrix exponentiation are much more efficient than recursion.

Given Fib(30) = 832,040 and Fib(28) = 317,811, what is Fib(29)?

Learn how to find Fib(29) using the Fibonacci sequence, given Fib(30) = 832,040 and Fib(28) = 317,811. This problem involves arithmetic and recursive properties of Fibonacci numbers, suitable for students in Grades 8-10.

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