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Please provide the step by step computation

The image shows an activity where you are tasked with continuing a Fibonacci spiral. The sequence starts at 1, and each subsequent number is the sum of the two preceding ones. The Fibonacci numbers start as follows:

1, 1, 2, 3, 5, 8, 13, 21, 34, ...

In this case, you need to continue the Fibonacci sequence and stop once \( n = 30 \) is reached.

The steps are:

1. The first two numbers are \( 1 \) and \( 1 \) (these are already assumed to be the first values).
2. The next number in the Fibonacci sequence is calculated as the sum of the last two numbers:

\[
1 + 1 = 2
\]

3. Continuing the pattern, each number is the sum of the last two numbers:
   
   - \( 1 + 2 = 3 \)
   - \( 2 + 3 = 5 \)
   - \( 3 + 5 = 8 \)
   - \( 5 + 8 = 13 \)
   - \( 8 + 13 = 21 \)
   - \( 13 + 21 = 34 \)

As seen in the image, we have \( 13, 21, 34 \) visible. We now continue:

4. \( 21 + 34 = 55 \)
5. \( 34 + 55 = 89 \)
6. \( 55 + 89 = 144 \)
7. \( 89 + 144 = 233 \)
8. \( 144 + 233 = 377 \)
9. \( 233 + 377 = 610 \)
10. \( 377 + 610 = 987 \)
11. \( 610 + 987 = 1597 \)
12. \( 987 + 1597 = 2584 \)
13. \( 1597 + 2584 = 4181 \)
14. \( 2584 + 4181 = 6765 \)
15. \( 4181 + 6765 = 10946 \)
16. \( 6765 + 10946 = 17711 \)
17. \( 10946 + 17711 = 28657 \)
18. \( 17711 + 28657 = 46368 \)
19. \( 28657 + 46368 = 75025 \)
20. \( 46368 + 75025 = 121393 \)
21. \( 75025 + 121393 = 196418 \)
22. \( 121393 + 196418 = 317811 \)
23. \( 196418 + 317811 = 514229 \)
24. \( 317811 + 514229 = 832040 \)

At this point, we have completed up to \( n = 30 \) where \( F(30) = 832040 \).

### Would you like more details on the spiral, or any clarification?

Here are 5 questions related to this problem:

1. How is the Fibonacci sequence connected to the golden ratio?
2. Can you apply the Fibonacci sequence to nature patterns such as plants or shells?
3. What is the formula for finding the \( n \)-th Fibonacci number using Binet's formula?
4. How does the Fibonacci spiral visually represent the Fibonacci sequence?
5. How is Fibonacci related to Pascal's Triangle?

**Tip:** The ratio between consecutive Fibonacci numbers approaches the golden ratio as the sequence progresses.

Learn how to compute the Fibonacci sequence up to n=30 using step-by-step calculations. Explore key mathematical concepts like the Fibonacci sequence, spiral representations, and its connection to the golden ratio. Ideal for students in Grades 6-10.

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