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Difference Sequence

Age 14 to 16 Short
Challenge Level

The first term in a sequence is 2016 and the second term is 2017.

Every other term is given by the difference between the two terms before it. So for example, the third term is the difference between 2016 and 2017, which is 1.

The $n^\text{th}$ term is equal to 2000; what is the value of $n$?

This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.