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Leonardo Pisano Bigollo known commonly as Fibonacci was born in Pisa around 1170 AD He...

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Leonardo Pisano Bigollo known commonly as Fibonacci was born in Pisa around 1170 AD He is best known for the Fibonacci sequence 1 1 2 3 5 8 13 21 which starts with 1 and 1 and then each subsequent term of the sequence is the sum of the preceding two terms 1 Can we write a formula for the general term un of the Fibonacci sequence 2 Can the Fibonacci sequence be written using a formula which connects successive terms of the sequence 3 Where do we see the Fibonacci sequence in nature 4a Calculate the ratio of consecutive terms of the Fibonacci sequence and so on Where appropriate round your answers to 5 decimal places b What do you notice about the values in a Research the golden ratio and its connection with the Fibonacci sequence

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