Tlangles Consider this sequence of diagrams The first diagra

Tlangles Consider this sequence of diagrams: The first diagram is made up of three line segments of equal length. You can think of the second diagram as made up of nine segments of that same length, and so on. Determine how you would find the number of segments of the given length for any diagram in the sequence.

Solution

For 1: 1*3

For 2: (1+2)*3

For 3: (1+2+3)*3

For 4: (1+2+3+4)*3

For n: (1+2+3+4+...+n)*3 = 3n(n+1)/2