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Given the general term of a sequence, find the first 5 terms as well as the $100^{\text {th }}$ term:
$$a_{n}=\frac{n(n-1)}{2}$$
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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.
$$a_{100}=\frac{100(100-1)}{2}=\frac{100(99)}{2}=\frac{9,900}{2}=4,950$$

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