Question: 1. Write the first ten terms of the Fibonacci sequence 2. Find the sum of the first ten terms of the Fibonacci sequence that you

1. Write the first ten terms of the Fibonacci sequence

2. Find the sum of the first ten terms of the Fibonacci sequence that you generated in problem 1. Divide the sum by 11. What do you notice?

3. Choose two numbers other than 1 and 1. The numbers do not have to be equal. Generate a Fibonacci-like sequence, beginning with these two numbers. Write the first ten terms of your sequence. For example, you could choose the numbers 5 and 6 and the first two numbers. The third term would be 11 (5 + 6), the fourth term would be 17 (6 + 11), and so on. Do NOT use 5 and 6 as your first two terms.

4. Find the sum of the sequence you created in problem 3. Divide the sum by 11. What do you

notice?

5. Make a hypothesis. What is special about the sum on the first ten terms of any Fibonacci-like sequence?

6. Create an example of the Fibonacci-like sequence beginning with two different numbers than you chose in problem 3. Do NOT use 5 and 6 as your first two terms. Write the first ten terms of your sequence. Does the hypothesis you wrote in problem 5 apply to this sequence?

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