Evenly Spaced Sets
Sequence of numbers whose value goes up or down by the same amount
All of the values in the set are multiples of the increment
All of the values in the set increase by 1 or consecutive amount.
Evenly Spaced Set: Property 1
Mean and Median are equal to each other.
Evenly Spaced Set: Property 2
Mean and Median of set are equal to avg of FIRST and LAST terms.
Evenly Spaced Set: Property 3
Sum of the elements in set equals avg number in set times the Number of Items in set.
Counting Integers: Be inclusive of extremes
+ 1 and Done. (Last - First + 1)
Counting Consecutive Multiples
(Last - First) / Increment + 1
Sum of Consecutive Integers
1. Avg First & Last term (First+Last/2) 2. Count Number of Terms (Last - First + 1) 3. Multiply middle number by the number of terms to find sum
Note of Sum of Avg of Odd number
Note of Sum of Avg of Even number
Products of Consecutive Integers & Divisibility
Product of K consecutive integers is always divisible by K factorial (K!)
Sums of Consecutive Integers & Divisibility - ODD
For any set of consecutive integers with an ODD number of items, the sum of all the integers is ALWAYS a multiple of the number of items.
Sums of Consecutive Integers & Divisibility - EVEN
For any set of consecutive integers with an EVEN number of items, the sum of all the items is NEVER a multiple of the number of items.
Consecutive Integers & Divisibility
Use prime boxes to track factors of consecutive integers.
Order of Operations