Presentation on theme: "Consecutive Integers Consecutive Integers are integers that follow one after another. Example 1: are consecutive integers."— Presentation transcript:
1 Consecutive IntegersConsecutive 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 Integers2) Consecutive Even Integers3) Consecutive Odd Integers
3 Consecutive IntegersConsider 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 IntegersWhat 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 IntegersAssume 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 2Increase by 2
8 Consecutive Even Integers Consecutive Odd Integers Notice the common pattern for the third integer:Increase by 4Increase by 4Note 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 consideringthree consecutive even integers, orthree 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: