In the sequence $1,3,2, \ldots$ each term after the first two is equal to the preceding term subtracted from the term that precedes it, that is: if $n>2$ then $a_{n}=a_{n-1}-a_{n-2}$. What is the sum of the first 100 terms of this sequence?
Let's initially write some terms:

$$
1,3,2,-1,-3,-2,1,3,2, \ldots
$$

The 7th and 80th terms are, respectively, equal to the 10th and 2nd terms. This means that the sequence repeats every 6 terms. The sum of the first 6 terms is $1+3+2-1-3-2=0$, and therefore, the sum of the first 96 terms is also 0. Thus, the sum of the first 100 terms of this sequence is equal to the sum of the last 4 terms, that is, $1+3+2-1=5$.