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 happened? 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 another 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? For problems 7-11 determine if the sequence is arithmetic, geometric, or neither. Explain your answer in 1-2 complete sentences. 7- 1, 4, 16, 25, 36, ... 8- 20, 18.5, 17, 15.5, 14, ... 9- 10, -9, 8, -7, 6, -5, 4, ... 10- 40, -10, 5/2, -5/8, 5/32, ... 11- 10, 8, 5, 1, -4, ... 8- For each sequence in problems 7-11 that is arithmetic, find the arithmetic sequence. Then answer the following questions. a) Write the arithmetic sequence. What is the common difference of the sequence? b) Write the mathematical expression that describes the arithmetic sequence. c) Use sigma notation to describe the sum of the first ten terms of the arithmetic sequence. d) Find the sum of the first ten terms of the arithmetic sequence. 9- For each sequence in problems 1-5 that is geometric, find the geometric sequence. Then answer the following questions. a) Write the geometric sequence. What is the common ratio of the geometric sequence? b) Write the mathematical expression that describes the geometric sequence. c) Use sigma notation to describe the sum of the first ten terms of the geometric sequence. d) Find the sum of the first ten terms of the geometric sequence. 10- Create your own arithmetic or geometric sequence. a. Write the first ten terms of your sequence. b. Explain why your sequence is either arithmetic or geometric. c. Write the mathematical expression that describes the arithmetic or geometric sequence. Then, use sigma notation to express the sum of the first ten terms of your sequence. d. Write the formula for and find the sum of the first ten terms of your sequence. Identify the n, a1, and values for d or r needed to find the sum