How are these numbers related to the fibonacci

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Unformatted text preview: e Friday 2/25) (Related to the Fibonacci Numbers) 1+ 5 . Verify that φ and 1 − φ are the two solutions of the quadratic 2 equation x 2 = x + 1, which can be written in standard form as x 2 − x − 1 = 0 . (a) Let φ = φ n − (1 − φ ) n € . Use a calculator or spreadsheet or other software to € € (b) Let Sn = 5 € € compute accurately the first 10 of the numbers Sn in this sequence. Write them down. How are these numbers related to the Fibonacci sequence? € (c) Use the sequence Sn to prove a formula for the nth Fibonacci number. € (d) Use this formula to calculate the 35th, 75th and 105th Fi...
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