standard_description: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
problem_activity: Task
Below are pictures of the first three  triangular numbers:
[IMG]
In general, the $n^{\text{th}}$ triangular number is the total number of dots in $n$ columns where the columns have $1, 2, 3, \ldots, n$ dots.
The following picture relates the first three triangular numbers to areas of rectangles:
[IMG]
Use this idea to calculate the seventh triangular number, $1 + 2 + 3 + 4 + 5+ 6+ 7$.
Calculate the hundredth triangular number, $1 + 2 + 3 + \cdots + 98 + 99 + 100$.
Find a formula for calculating the $n^{\text{th}}$ triangular number, $1 + 2 + \cdots + (n-1) + n.$


aligns: no