Consecutive Integers

Things one must know:

• Sets of consecutive integers are sets of consecutive multiples, a special case of evenly spaced sets, where all the values in the set are multiples of the increment.
• The arithmetic mean and median are equal to each other.
• The mean and median equal the average of first and last terms of the set.
• The sum of elements in the set is equal to the arithmetic mean times the number of items in the set. 
• The sum of a set of an odd number of consecutive integers is divisible by the number of items.
• The sum of a set of an even number of consecutive integers is never divisible by the number of items.
• Counting consecutive integers: Last - First + 1
• Counting consecutive multiples: (Last - First) / Increment + 1
• The product of n consecutive integers is always divisible by !n