GOLDEN RATIO One of the most famous sequences is called the Fibonacci Sequence. This sequence begins with a. = 0, a1 = 1, and continues by adding the two previous values together. Search Wolfram | Alpha for "Fibonacci" 1. Fill in the table below listing the first twenty terms of the Fibonacci Sequence. Wolfram| Alpha provides these for you when you select to use Fibonacci as a math function. n 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 19 20 value 0 2. Define the nth term of the Fibonacci Sequence using a recursive relation: 3. Find the ratio of consecutive terms of the Fibonacci Sequence by dividing the (n+1)" term by the nth term. Round values to 3 decimal places. What value is this ratio getting close to? a) 93 = b) - 6 = c) - 29 = as a 8 a1 e) - "15 = f) -18 = 3) 20 a14 a17 a19 4. Use Wolfram | Alpha to search "Golden Ratio." Explain how the Golden Ratio is related to Fibonacci's Sequence. The golden ratio has been found to be aesthetically pleasing and can be found in art, architecture, nature, and music. Each of the shapes below illustrate the golden ratio in some form and in each case, the ratio a ath = holds true. Find the value for b in each case. a =5 b a = 8 a+ b Suggestions: Find artwork, architecture, music, or items in nature that can be modeled using the golden ratio. Sequences, Series, and Probabilities 36 Activities Using Wolfram Alpha