Find the sum of the first ten Fibonacci numbers.


The Fibonacci sequence is defined such that each number is the sum of the two preceding ones, starting from 0 and 1. The first ten Fibonacci numbers are:

1. \( F_1 = 1 \)
2. \( F_2 = 1 \)
3. \( F_3 = 2 \)
4. \( F_4 = 3 \)
5. \( F_5 = 5 \)
6. \( F_6 = 8 \)
7. \( F_7 = 13 \)
8. \( F_8 = 21 \)
9. \( F_9 = 34 \)
10. \( F_{10} = 55 \)

To find the sum of the first ten Fibonacci numbers, we add these values together:

\[
1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 = 143
\]

Thus, the sum of the first ten Fibonacci numbers is **143**.

Would you like more details or have any questions? Here are some related questions:

1. How is the Fibonacci sequence defined recursively?
2. What is the formula for the \(n\)-th Fibonacci number?
3. Can you find the sum of the first 20 Fibonacci numbers?
4. What are some interesting properties of the Fibonacci sequence?
5. How does the Fibonacci sequence relate to the golden ratio?

**Tip:** The sum of the first \( n \) Fibonacci numbers is one less than the \((n+2)\)th Fibonacci number, i.e., \( F_1 + F_2 + \dots + F_n = F_{n+2} - 1 \).

Discover how to find the sum of the first ten Fibonacci numbers step-by-step. Learn about the Fibonacci sequence and its properties. Suitable for students in Grades 7-9.

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