Answer: [tex]a_{n} = r^{2} - r(\frac{r-1}{2} )[/tex]
r is the row number
a (sub n) is the amount in any given row number, n
To find the number of balls in a row, start by getting the square of the row.
Then take the row number minus 1, and divide by 2. Multiply that factor times the row number. That will produce a number to be subtracted from the square.
The square of the row number minus the row number times the factor will produce the number of balls.
Step-by-step explanation: Chart of values attached. Also reposting the pdf from your question as it did not appear in my original view
We know that the number of balls in the row is the number from the previous row plus the row number. So I made a chart of the first 10 values
The solution depends on seeing a relationship between the row numbers and the output of balls in the stacks. It helped to create a diagram with balls stacked vertically and horizontally to see the "square of the number minus some quantity"
