Answer:

Triangle Numbers
Rows	Triangle(Rows)	Formula
1	1	base case
2	3	2 + Triangle(1)
3	6	3 + Triangle(2)
4	10	4 + Triangle(3)
5	15	5 + Triangle(4)
6	21	6 + Triangle(5)
7	28	7 + Triangle(6)

Formula for Triangle Numbers

The table shows values of the Triangle() function. For example, Triangle(4) = 10. But it stops at seven. What is Triangle(12)?

We have figured out that the following is true:

total number of pins in N rows = number of pins in row N + 
                                 total number of pins in N-1 rows
                           
                               = N + total number of pins in N-1 rows

This can be written as a formula:

Triangle( N ) = N + Triangle( N - 1 )

So the number of pins in a 12 row arrangement is 12 + number of pins in 11 rows.

QUESTION 4:

How many pins are in 11 rows?