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Name:_________________________ Alg. 2 Extra Credit (10 points max): Answer the following questions. SHOW ALL WORK for full points! You will be graded on completeness, accuracy and originality. FIBONACCI EXTRA CREDIT The famous Fibonacci sequence is a sequence where you add the previous 2 numbers to get the next number. The first fifteen Fibonacci numbers are: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 1. What sort of number is every third term? 2. Choose any three consecutive Fibonacci numbers. Multiply the first by the third. Square the second. Repeat this for other groups of three. What do you notice? 3. 4. Choose any four consecutive Fibonacci numbers. Multiply the first by the fourth. Multiply the second by the third. Repeat for other groups of four. What do you notice? 5. If T1 = first term, T2 = second term, T3 = third term and so on: a) Find the sum of the first four terms. Compare the total with T6. b) Add the first five terms. Compare the total with T7. c) Add the first six terms. Compare the total with T8. d) Without adding, find the sum of the first 12 terms. (explain your answer) 5. Research and find 4 different areas in life where the Fibonacci sequence numbers are found. Explain. 1) 2) 3) 4)