We have a sequence of 100 positive integers. The average of the first and second numbers is 1. The average of the second and third numbers is 2. The average of the third and fourth numbers is 3. This pattern continues, and the average of the 99th and 100th number is 99. What is the 100th number?

Clarification: Apart from being positive integers, there is no restriction placed on this sequence. In particular, they need not be an increasing sequence, need not be pairwise distinct, need not be all even, etc.

Question

We have a sequence of 100 positive integers. The average of the first and second numbers is 1. The average of the second and third numbers is 2. The average of the third and fourth numbers is 3. This pattern continues, and the average of the 99th and 100th number is 99. What is the 100th number?

Clarification: Apart from being positive integers, there is no restriction placed on this sequence. In particular, they need not be an increasing sequence, need not be pairwise distinct, need not be all even, etc.