To solve \( 2F_{25} + F_{30} \), we need to calculate the values of the 25th and 30th Fibonacci numbers, where the Fibonacci sequence is defined by:

\[
F_n = F_{n-1} + F_{n-2}, \quad F_0 = 0, \quad F_1 = 1
\]

Now, let's compute \( F_{25} \) and \( F_{30} \):

- \( F_{25} = 75,025 \)
- \( F_{30} = 832,040 \)

Using these values, we can now compute the expression:

\[
2F_{25} + F_{30} = 2(75,025) + 832,040 = 150,050 + 832,040 = 982,090
\]

Thus, \( 2F_{25} + F_{30} = 982,090 \).

Would you like more details on the Fibonacci sequence, or any further explanations?

---

Here are 5 related questions to deepen your understanding:
1. How is the Fibonacci sequence defined recursively?
2. What is the 50th Fibonacci number?
3. How can you calculate Fibonacci numbers efficiently for large indices?
4. What is the ratio between consecutive Fibonacci numbers, and why is it important?
5. How does the Fibonacci sequence relate to the Golden Ratio?

**Tip**: Fibonacci numbers grow exponentially, so using approximation formulas (like Binet's formula) can be useful for very large indices.

Learn how to calculate the expression 2F25 + F30 by applying the Fibonacci sequence. This problem demonstrates the recursive nature of Fibonacci numbers and their practical computation. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation