Consecutive IntegersIntegers that follow one another from a given starting point, without skipping any integers. 3, 4, 5, and 6 are consecutive integers but 3, 5, 6, and 14 are not.
Consecutive Even Integers2, 4, 6, 8, etc.
Consecutive Odd Integers1, 3, 5, 7, etc.
Consecutive Multiples4, 8, 12, 16 (multiples of 4); this is a special case of an evenly spaced set.
Evenly Spaced SetA set of numbers in which each number is a set distance, or increment, from the next. 1, 4, 7, 10 is an evenly spaced set with an increment of 3. In any evenly spaced set:
The arithmetic mean (average) is equal to the median. The set comprising 1, 2, 3, 4, and 5 has a mean of 3 and a median of 3.
The mean and the median of the set are both equal to the average of the first and last terms in the set. For the set {1, 2, 3, 4, 5}, the first term is 1 and the last term is 5. The average of these two terms is 3, which also equals both the median and the mean of the entire set.
The sum of the elements in a set equals the mean multiplied by the number of items in the set. For the set {1, 2, 3, 4, 5}, the mean is the middle term, 3. There are five terms in the set, so the sum is 3*5 = 15.
InclusiveGiven "a set of integers between15 and 19 inclusive," we include the numbers 15 and 19 in the set: {15,16,17,18,19}. Given "a set of integers between 15 and 19," we do not include 15 and 19 in the set: {16,17,18}.
Product of n consecutive integers and divisibilityThe product of n consecutive integers is always divisible by n! Given 6*7*8*9, we have n = 4 consecutive integers. The product of 6*7*8*9, therefore, is divisible by 4! = 4*3*2*1 = 24.
Sum of n consecutive integers and divisibilityThere are two cases, depending upon whether n is odd or even:
If n is odd, the sum of the integers is always divisible by n. Given 6+7+8, we have n = 3 consecutive integers. The sum of 6+7+8, therefore, is divisible by 3.
If n is even, the sum of the integers is never divisible by n. Given 6+7+8+9, we have n = 4 consecutive integers. The sum of 6+7+8+9, therefore, is not divisible by 4.
