**Answer:**

First five terms: $0,1,3,6,10 ; a_{100}=4,950$

**Explanation:**

To find the first 5 terms, substitute $1,2,3,4$, and 5 for $n$ and then simplify.

$$

\begin{array}{l}

a_{1}=\frac{1(1-1)}{2}=\frac{1(0)}{2}=\frac{0}{2}=0 \\

a_{2}=\frac{2(2-1)}{2}=\frac{2(1)}{2}=\frac{2}{2}=1 \\

a_{3}=\frac{3(3-1)}{2}=\frac{3(2)}{2}=\frac{6}{2}=3 \\

a_{4}=\frac{4(4-1)}{2}=\frac{4(3)}{2}=\frac{12}{2}=6 \\

a_{5}=\frac{5(5-1)}{2}=\frac{5(4)}{2}=\frac{20}{2}=10

\end{array}

$$

Use $n=100$ to determine the $100^{\text {th }}$ term in the sequence.

$$

a_{100}=\frac{100(100-1)}{2}=\frac{100(99)}{2}=\frac{9,900}{2}=4,950

$$