The Fibonacci sequence is defined as:

$F(1) = 1, \quad F(2) = 1$ $F(n) = F(n-1) + F(n-2) \quad \text{for} \quad n > 2$

The 67th term in the Fibonacci sequence can be found using the recursive formula or by using a faster method, such as matrix exponentiation, or utilizing a direct formula known as Binet's formula.

For large Fibonacci numbers like the 67th term, it’s more efficient to compute it iteratively or using a pre-built algorithm.

Let me compute that for you. Let's calculate the 67th Fibonacci number using an iterative approach. def fibonacci(n): a, b = 0, 1 for _ in range(n): a, b = b, a + b return a

Find the 67th Fibonacci number

fibonacci_67th = fibonacci(67) fibonacci_67thThe 67th term in the Fibonacci sequence is 44,945,570,212,853.

Let me know if you'd like a deeper explanation of how this is calculated or if you have any more questions!

Here are some related questions for further exploration:

1. How can you calculate Fibonacci numbers using Binet's formula?
2. What are some applications of the Fibonacci sequence in nature and technology?
3. How does the time complexity of different methods for calculating Fibonacci numbers compare?
4. What is the relationship between Fibonacci numbers and the golden ratio?
5. How do recursive and iterative methods for Fibonacci differ in terms of efficiency?

Tip: Fibonacci numbers grow exponentially, so methods like matrix exponentiation or using closed-form expressions can save time for large terms!