Balancing Numbers
Consider the set of natural numbers 1 to 8. For this set of numbers, 6 is called the balance because the numbers before 6 add up to the same sum as the numbers after 6. In other words, 1+2+3+4+5 = 7+8.
Triangular and Trapezoidal Numbers
Triangular numbers and trapezoidal numbers are both natural numbers that can be expressed as the sum of more than one consecutive natural numbers.