3. A row contains 2015 positive numbers. The product of all the numbers is 2015, and the product of any three consecutive numbers is 1. What is the 1008th number in the sequence?

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# Solution

From the additional condition, it follows that if the sequence is divided into blocks of 3 numbers "end-to-end," moving simultaneously from left and right towards each other, the 336th block from the left and the 336th block from the right will overlap on the middle number. Let's denote this number as $C$.

Then the product of all the numbers, on one hand, is 2015, and on the other hand, it is $1 / C$. Therefore, $\quad C=\frac{1}{2015}$.

Answer. The 1008th number in the sequence is $\frac{1}{2015}$.