Consecutive Integers

1. Consecutive Integers Consecutive Integers are integers that follow one after another. Example 1: are consecutive integers.

2. In Algebra we sometimes are presented with a problem that requires a pattern of consecutive integers. The patterns are usually one of three types: 1) Consecutive Integers 2) Consecutive Even Integers 3) Consecutive Odd Integers

3. Consecutive Integers Consider the example given earlier: Given the first integer 8, what would be necessary to determine the next integer of 9? Simply add 1 to the 8 to give: Add 2 to the 8 to get the next integer 10:

4. Consecutive Integers What if the first integer is unknown? Let x represent the first integer. Simply add 1 to get the second integer. Add 2 to get the third integer.

5. Consecutive Integers Assume that we are considering three consecutive integers, and do not know the first integer. The pattern is given by: Example 2: Now assume that we know the first integer is 17. The integers are …

6. Consecutive Even Integers Consecutive Odd Integers Consecutive even integers and consecutive odd integers will be considered together since they are related. Consecutive Even Integers: Consecutive Odd Integers:

7. Consecutive Even Integers Consecutive Odd Integers Notice the common pattern for the second integer: Increase by 2 Increase by 2

8. Consecutive Even Integers Consecutive Odd Integers Notice the common pattern for the third integer: Increase by 4 Increase by 4 Note that it is the first integer that determines the pattern of even or odd.

9. Consecutive Even Integers Consecutive Odd Integers Assume that we are considering three consecutive even integers, or three consecutive odd integers, and do not know the first integer. Both patterns are given by:

10. Example 3: Write the pattern for three consecutive odd integers: Determine the integers if the first integer is -7:

11. END OF PRESENTATION