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Ci Hui from Queensland Academy for Science Mathematics and Technology (QASMT) in Australia, Tanish from Pate's Grammar School in the UK and Julia S from the UK all found the powers of $\bf Q$ and noticed a pattern. Click to see Ci Hui's calculations:
And click to see what Ci Hui noticed:
Tanish used algebra to show why this happens:
Julia used proof by induction to show the terms will always follow the Fibonacci sequence: