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Attatched are the triangular numbers used to do the problem, and a table clarifying a few things.

The $\displaystyle n$ row on the table states what n equals.

The $\displaystyle T_n$ row states how many dots there are when $\displaystyle n$ = a certain number.

I am to find a formula for the $\displaystyle n^{\text{th}}$ triangular number.

$\displaystyle \begin{array}{c|cccc} n &\quad 1 & \quad2 & \quad3 & \quad4 \\ \hline

& & & & \quad\bullet \\

& & & \quad\bullet & \quad\bullet\:\bullet \\

& & \quad\bullet & \quad\bullet\:\bullet & \quad\bullet\:\bullet\:\bullet \\

& \quad\bullet & \quad\bullet\:\bullet & \quad\bullet\:\bullet\:\bullet & \quad\bullet\:\bullet\:\bullet\:\bullet \\ \hline

T_n & \quad1 & \quad3 & \quad6 & \quad10

\end{array}$