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A Fibonacci Question

I stumbled upon the interesting question below from the TeamMathics Facebook page:

Question of the day:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,…

If this Fibonacci sequence continues for 2016 terms, what is the last digit (unit value) when you add all the 2016 numbers?


*A possible solution is shown in the attached image below (I could be wrong though):


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