Find the 15th term of the Fibonacci sequence if the 10th term and 11th terms are 34 and 55 respectively

To find the 15th term of the Fibonacci sequence, we can use the information provided: the 10th term is 34, and the 11th term is 55. The Fibonacci sequence is defined by the recurrence relation:

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

Given:
- \( F(10) = 34 \)
- \( F(11) = 55 \)

We can calculate the subsequent terms:

\[
F(12) = F(11) + F(10) = 55 + 34 = 89
\]
\[
F(13) = F(12) + F(11) = 89 + 55 = 144
\]
\[
F(14) = F(13) + F(12) = 144 + 89 = 233
\]
\[
F(15) = F(14) + F(13) = 233 + 144 = 377
\]

Thus, the 15th term of the Fibonacci sequence is **377**.

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions you might find interesting:
1. What is the 20th term of the Fibonacci sequence?
2. How do you derive the general formula for the nth term in the Fibonacci sequence?
3. Can you prove that the Fibonacci sequence grows exponentially?
4. What is the sum of the first 15 terms of the Fibonacci sequence?
5. How can the Fibonacci sequence be applied in real-life scenarios?

**Tip:** The ratio of consecutive Fibonacci numbers approximates the Golden Ratio (\(\phi \approx 1.618\)) as the sequence progresses.

Learn how to find the 15th term of the Fibonacci sequence using the given 10th and 11th terms (34 and 55 respectively). This problem involves applying the Fibonacci sequence formula recursively to compute subsequent terms. Suitable for high school students studying sequences and series.

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