In the sequence of letters $$\text{KANGAROOKANGAROOKANG}\cdots$$ the word $$\text{KANGAROO}$$ is repeated indefinitely. What is the $$2017\text{th}$$ letter in this sequence? 
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The sequence $$\text{KANGAROOKANGAROOKANG}\cdots$$ repeats every $$8$$ letters. Since $$2017=8\times252+1$$, the $$2017\text{th}$$ letter in the sequence is the first of the repeating sequence and hence is $$\text{K}$$. 