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This is straightforward but care must be taken to explain the significance of both roots of the quadratic equation. Also you must prove both the 'if' and the 'only if', that is, for general Fibonacci sequences, 'if the first two terms are in the golden ratio then the sequence is geometric' and 'if the sequence is geometric then the ratio of successive terms is the golden ratio'.
Induction is required
Golden Fibs
Age 16 to 18
Challenge Level 
This is straightforward but care must be taken to explain the significance of both roots of the quadratic equation. Also you must prove both the 'if' and the 'only if', that is, for general Fibonacci sequences, 'if the first two terms are in the golden ratio then the sequence is geometric' and 'if the sequence is geometric then the ratio of successive terms is the golden ratio'.
Induction is required
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