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answerhappygod
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SOLVE USING PYTHON:
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3. The Fibonacci Sequence is defined by the following recursive relation: fn fn-1 + fn-2, n ≥ 2 = with initial values: fo=f1 = 1 a) Use a for loop to generate the first 11 terms (fo, f₁,..., ƒ10). q² = b) If q satisfies satisfies q² = q + 1 and we define an q", then we can show that an = an-1 + an-2. In this case, we say that sequence an has the same recursive relation as the Fibonacci Sequence. Find all possible values of q that satisfies q² = q + 1. (NOTICE that you should find two such q values, denoted by 9₁ and 92.) c) Let c₁ and c₂ be two numbers. If we define bn = C₁97 + c292, then it can be shown that bn = bn-1 +bn-2. Find the proper values of c₁ and c₂ such that bo fo and b₁ = f₁, then compute the first 11 terms bo, b₁,..., b10. = d) compare the first 11 terms of fn and bn, what can you conclude? Does fn bn for all n and why?
3. The Fibonacci Sequence is defined by the following recursive relation: fn fn-1 + fn-2, n ≥ 2 = with initial values: fo=f1 = 1 a) Use a for loop to generate the first 11 terms (fo, f₁,..., ƒ10). q² = b) If q satisfies satisfies q² = q + 1 and we define an q", then we can show that an = an-1 + an-2. In this case, we say that sequence an has the same recursive relation as the Fibonacci Sequence. Find all possible values of q that satisfies q² = q + 1. (NOTICE that you should find two such q values, denoted by 9₁ and 92.) c) Let c₁ and c₂ be two numbers. If we define bn = C₁97 + c292, then it can be shown that bn = bn-1 +bn-2. Find the proper values of c₁ and c₂ such that bo fo and b₁ = f₁, then compute the first 11 terms bo, b₁,..., b10. = d) compare the first 11 terms of fn and bn, what can you conclude? Does fn bn for all n and why?