1. In the increasing sequence $1,3,4,9,10,12,13, \cdots$, it includes all positive integers that can be written as the sum of distinct powers of 3. What is the value of the 100th term in this sequence?
II. 1.981.
Since this sequence includes all positive integers that are powers of 3 and sums of different powers of 3, the numbers in this sequence are represented in ternary (base-3) notation using only the digits $1$ and $0$.

Given that 100 in binary is represented as $(1100100)_2$, and the 100th term of the sequence is obtained by interpreting this binary number as a ternary number, the result is $3^6 + 3^5 + 3^2 = 981$.