# Doro68: 1.4 Consective Integers Strategy

## 16 terms

### Evenly Spaced Sets

Sequence of numbers whose value goes up or down by the same amount

### Consecutive Multiples

All of the values in the set are multiples of the increment

### Consecutive Integers

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

Integer

Non-Integer

### 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.

P.E.M.D.A.S.